mounted after a week of groundwork, and can now w/t and sometimes canter under saddle. Unfortunately she has come up sore.
If she's only 3yo I would be doing very little riding on her, no trotting or cantering yet, for at least another couple of years at least. A horse's vertebral growth plates don't 'close' until around 6yo at least.
Anyway it could be because of an ill fitting saddle, so I am going go get a fitter out in April too.
Yes, if you're going to do any riding in a saddle & you're not sure, definitely good to get a *good* saddle fitter to fit her, or get the chiro to evaluate her saddle when they're out. But remember she's only 3yo & still growing, so no matter how great a saddle fit you may get now, you'll have to check/adjust it frequently - every couple of months I suggest.
Anyway she already know a few tricks (kiss, smile and lift her leg when tapped and asked) the leg will turn into Spanish walk eventually. But I'm thinking of teaching her with the clicker to fetch, kick a ball, say yes and no, hug, lay down (this one will be easy since she loves rolling). Any other tricks?
Your imagination's the limit! Just keep safety in mind - hers too, in what/how you teach. If she lays down/rolls over by herself, I'd say teaching her to do it on cue wouldn't likely be bad for her back, but if she doesn't do it of her own accord, I second that it may be an indication you shouldn't ask for this until her back's better.
She seems fine to lunge, I will most likely be doing that once a week
Lunging is an exercise that is quite hard on joints, especially of immature, unfit beasties. Of course, it depends how you do it, but I would consider that carefully & not overdo it. Little & often is far better than big sessions too, especially if you can only do it once a week.