Questions on how to set up a new mount / animal companion

So me and my friends have recently started a modified version of Rise of the Runelords(pls no spoilers), and when we went on a boar-hunting trip my character(a kobold barbarian) decided to capture and tame one of the wild boars to use as a mount. My character ended up succeeding in taming the boar and now I need to make a character sheet for the boar. I've already written in most of the basic stats but I cant seem to find anything for mounts on leveling up, what skills to put down, taking feats, how or if I should roleplay an animal, what actions I need to roll animal handling for, how to teach them tricks, what do I not need to teach them or roll for, etc. So if anyone has any info or guides on how to set up and use mounts and animal companions it would be greatly appreciated. Thanks ahead of time.

Unless you take levels in something to make it an animal companion, nothing happens when you level up. A boar remains a boar.

If you do take levels in Druid or Hunter (or possibly other that I am forgetting), then it gets the basic stats for an animal companion modified by the boar animal companion entry (which might be a slight downgrade in the short term, but the GM might waive that since you went to the trouble of finding the animal first). EDIT: The "basic stats" I refer to are a table under the druid entry, which gives stats for each level, so the animal companion levels up when you do and in much the same, based on your effective Druid level.

EDIT2: Ranger was the one I was forgetting. Also Cavalier but they are limited in the animals they can take and boar is probably not among them. And various archetypes. If there is a barbarian archetype that grants an animal companion, retraining into that might be your best bet!

Hope this helps.

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Unless you take levels in something to make it an animal companion, nothing happens when you level up. A boar remains a boar.

I'm planning on putting points in the Mad Dog subclass when I level up which allows me to have an animal companion. But since right now my character is just a vanilla barbarian, is he actually able to tame or employ an animal companion or mount at all? What are the restrictions I am working with until level 2? At this point is my boar just a boar that happens to follow me around where I have to make handling checks for every single action? Until he becomes officially an animal companion, how do I play this boar?

Animal Companion is a class feature; so if you do not have the feature, you do not have an animal companion. However, if you have the Handle Animal skill (and you presumably do or you would not have got this far), you can train an animal for riding (or other things using it).

Even after he becomes an animal companion, you will still need to make checks to order him around, but it will be a free action (instead) and you will get a +4 bonus so unless you have a Cha penalty or the creature is wounded, you only need two ranks before you cannot fail.

If it is not an AC, then commanding it is a move action, and you need six ranks before you cannot fail (assuming no Cha bonus or penalty).

I do not think you need to make checks to move a mount you are riding, but it is bedtime here so I am not going to check now! Maybe someone else will chime in.

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Also how can I teach my boar tricks that take weeks to learn when the campaign is run on an in-game day to day basis? If I want to teach my boar the "Attack" trick, which takes a week to learn, how do I go about teaching that in this kind of campaign where time only fast-forwards while we sleep? Do I just announce that I'm teaching a trick that takes a week, wait a whole week of activity with a boar that's dead weight(which would be across multiple sessions), and finally have one trick learned after 7 days? Is there a faster way to teach tricks? Do animal companions automatically start out with any tricks?

there are magic items that 'teach' the animal a set of tricks (decided on when creating the item)
-but yea, getting a wild animal to not only follow you but attack only specific creatures (and NOT attacking others) need a bit of effort...

class given animal companions do start with a few 'free' tricks already learned. and they are not counted for when considering the maximum amount of trick the animal can learn.

Ask your GM if you can switch to the Monted Fury archetype.

Ask your GM if you can switch to the Mounted Fury archetype.

I do not think you need to make checks to move a mount you are riding, but it is bedtime here so I am not going to check now! Maybe someone else will chime in.

Having looked a bit further, it is still not clear to me whether you need to make handle animal checks for a mount in addition to any ride check you might have to make. So maybe have a chat with your GM. EDIT: If it was me, I would say no in the interests of expedience.

Also how can I teach my boar tricks that take weeks to learn when the campaign is run on an in-game day to day basis?

You need downtime. Lack of downtime will hurt lots of characters; not just animal trainers. If you don't getting any from time to time, again you need to talk to the GM.

I'm planning on putting points in the Mad Dog subclass when I level up which allows me to have an animal companion.

"Putting point into [...] subclass" is not really meaningful in the context of Pathfinder, but it seems like you are talking about the Mad Dog Barbarian archetype. It affects you from first level, so you cannot just take it as second. You would have to retrain your first level from normal Barbarian to Mad Dog Barbarian (which again takes downtime). OTOH, since it is early in the campaign, your GM might allow you to tweak your character without formally retraining it.

Again, and this is becoming something of a theme for this post, have a talk with your GM about it.

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glass.