I have been DMing a campaign for the last few years that has downtime as an instrumental part of game play. Basically they run 2-3 adventures each month with the remainder of the 4 weeks of the month doing downtime activity. So I have some advice to make it fun and get the players involved.

First off I would look at the DMG, Xanathars Guide to Everything and Acquisition Inc source books because they all have rules for running downtime. That includes charging for lifestyle expenses and methods to make money. I would use those as the basis for what you are going to have the players do. The basics are do activity, risk money, make skill check(s) and get something back if pass or lose it if failure. What I do is just ask the players what they want to do and then debate / collaborate to getting this tied into one of the options. I wouldn’t do it weekly as suggested in the book but rather a few times. That way the players can change their world this their two years and maybe make or lose (just as fun) money.

As for the ritual spells the wizard could realistically get all of those spells if they had the money (they likely don’t) or the time (which they will). So I would use the spell scrolls costs to allow them to buy whatever scrolls they want and then copy it in the book. If realistically they can’t buy the scrolls they might need to get charged extra to import it or spend time traveling to a larger city to buy them both of which will cost them extra. The amount of gold they have will limit what they can buy.

Just note that while its possible to get lots of lower level ritual spells with time the costs for higher level spells gets difficult to purchase. The wizard should be spending their money on spells and getting scrolls and spell books are fun for wizard players.

If you are worried about they using it make sure to track time in dungeons and other locations. It takes 10 minutes to cast these spells which eats into durations for other spells. I also make sure I account for time to move through a dungeon. I use 120 ft. (4x movement speed on average) for new territory for 10 minutes. They can move faster (10x) over terrain they have covered before since they aren’t on the lookout for traps and monsters. I even roll for random monsters if appropriate in dungeons (typically 5-10% chance for one to appear) which forces people to take time into account. Its way more fun because they have to balance things. Do they want to keep their hour long spell up or waste their last 10 minutes casting Detect Magic as a ritual. These are fun decisions for a player to make.

Maybe I missed it, but are you allowing all players to pick something up during this time jump? I think that needs to be answered before I would be able to answer. If it’s just this player, I would say that it’s a time jump and not being treated as down time, but that you’ll keep this list in mind as you prepare rewards/loot for future sessions. If all players are getting downtime activity options then all you have to do is figure out how much downtime activity you’re allotting to them.

I’d say your instincts are good, and that this is too many rituals to give out. In fact, this looks more like a list of all rituals than a player’s wishlist of rituals.

You’ve got some good advice here on how many to allow, so let me take a different tack here and give some advice for handling a lot of rituals at once.

The foremost important rule of a ritual is that it takes ten minutes longer to cast a spell as a ritual than to simply cast the spell.

Many of these spells have a duration of one hour. Say you have three rituals going: comprehend languages, floating disk, and unseen servant. Every hour you would have to rest for 30 minutes to refresh your spells, then you’d have another 30 minutes of adventuring before they begin to expire.

So if your player wants to have the rituals active and ready, the entire party only travels at half speed. I’d have NPCs take the piss out of them and I’d encourage the players to do the same (in character, and all in good fun)

Time is important to you as a DM because you can use it to put pressure on the party. You can do this narratively by imposing deadlines, or taking NPCs hostage, or what have you. However, you can also impose this mechanically by having random encounters.

As the DM you get to decide how to do random encounters. The most common rule I see is to roll once per hour to see if there’s an encounter.

Now, a lot of this sounds like you might be punishing the player for using too many rituals. That’s not strictly true though. You’re enabling the player to make choices, and choices have consequences. Enforcing these rules are a way that you can be the Yes DM you want to be while also keeping the power level grounded.

tl;dr If they haven’t added any spells beyond what they get from leveling up, I’d say 4-7 is a fair baseline, but generally I would limit it to 1st and 2nd level spells.

Given that it’s a time jump, the way I would handle it is that whatever they’re gaining is basically through downtime, not adventuring (because if there was adventuring we wouldn’t be time skipping). So then you have to decide how comfortable you are with how many, if any, magic items you want the party to be able to gain through downtime (I’m going to treat them as obtaining the items through scrolls even though they could also get them from other spellbooks, because there’s just not much rules guidance for obtaining spellbooks, and this is a pretty big ask). Given that most downtime activities are broken down into weeks and you’re dealing with a couple years, I would probably instead take their actions by months or even seasons and multiply the results accordingly, so as to avoid spending literal hours just to adjudicate one player’s downtime.

Another thing to consider is if they found any spells they could add to their spellbook during the initial adventure. My quick and dirty guideline is +1 spell found in the world per level up, so if they haven’t added an extra 4 spells to their book so far, I’d approve 4 of their choice at a minimum. Lastly I’d consider how many magic items the party has encountered so far. If they haven’t found any scrolls or spellbooks, I’d say two 1st-level spells and maybe one 2nd-level spell would be fair compensation.

For a simpler version, you could just use the scroll prices from the back of Xanathar’s guide, and leave it up to them to come up with the money, either with what they have now or through downtime in the time skip (don’t forget that it also costs money to copy scrolls into a spellbook and there is a chance of failure).

For reference, the Xanathar’s scroll prices are:
1st-level: 75 gp
2nd-level: 150 gp
3rd-level: 300 gp

Rituals are ordinary spells, aren’t they? The character gets something like two spells per level, or transcribes extra spells from scrolls for some significant amount of money+time. In the 5e sourcebook it’s described in the section titled “adding spells” IIRC.

So no, you are not being strict. Unless the character gains 7 levels or has a tonne of cash, they aren’t following the rules.

Want book are you going off of? I would write them down and make scrolls available or have him pay gold to have a random wizard teach him. I dont think it’s unreasonable but i would make it cost. Also time is another thing that would keep him from being able to use them. Also mats cost to so wouldnt be to bad. Can you tell more about your campaign?

Say what you wrote first. That is the important part, and in game justifications exist to reinforce that.

In game reasons not to allow more than a few:

• how easy is it to learn new spells?
• can the character even afford to learn that many spells at level 5 (both inscribing and probably needing to pick up another spellbook or two which isn’t cheap).

Are the characters leveling up during the downtime? If not, they aren’t likely to be doing thibgs thst earn a lot of money beyond lifestyle costs. Sure, the wizard is probably doing research, but adding spells is a separate thing or all wozeds would have a ton of ritual spells.

I’d let them pick 2 or 3 max, about one per year of downtime.