Congrats on the new bun and welcome!
So, for litter training, you will likely continue to see that type of marking until he’s neutered (and his hormones have time to settle, usually about 2-3 weeks). Many buns will also choose to use a digging box as a litter box, so it may be best to remove it until he’s neutered and then try again, or convert it to something that is kind of a hybrid digging and litter box. Usually it’s recommend to keep the space somewhat restricted until he’s neutered for that reason as well. If the room he is exploring is very large and there is a spot he always toilets, you should add another litter box to that location.
As far as completely free-roaming, that depends a lot on your home and the bunny. Some bunnies are never suitable for 100% free-roam (by that I mean they are in a large area of the home 24/7) because they are too prone to getting into trouble, no matter how good the bunny-proofing is. I would probably wait at least until he’s neutered for the reasons I mentioned above. Once his litter box habits are good in a smaller area, you can start slowly increase the amount of space he gets while supervised. Then you can gradually allow him unsupervised time in some areas. There may be a situation where there is 1 room he is allowed 24/7 access to, and other rooms that he only gets to explore while you are with him. You may find that he was fine for a while in a room unsupervised and then one day decides to burrow into the couch (this happened to me with one of my buns LOL). Having some areas only available to the bun while supervised can actually be a benefit though because it makes the other rooms more exciting and he will continue to explore them. 🙂 There are cases where a bun gets 100% free roam and they no longer feel the need to go an explore (this happened with my buns). I have found a good balance to be free-roam while I’m home and awake, and the buns get penned when I’m not home or asleep. I also bring this up because I have seen many buns surrendered to shelters because the owner wanted to do 100% free roam, and then the bun was destructive, and rather that re-assess the housing they surrendered the bun to the shelter.
As far as the poops, young buns sometimes produce excess cecotropes because they get more pellets, so it’s pretty normal that you see that occasionally. Once he hits 6 months you can start reducing his pellets a little (he should be getting unlimited or near unlimited alfalfa-based pellets at this age) and then there should be less cecals.
One last comment, that you didn’t ask but thought I would share. Don’t be alarmed if he goes a bit nuts at around 4-6 months. It sounds like he’s already starting to hit puberty so you may already be noticing some extra hormonal behaviors. If my math is correct he’s almost 4 months now. You can check to see if his testicles have descended, once they do he can be neutered.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.