Wood conditioner should be put down before stain, to help even out the stain's penetration.

If it were me, I'd sand off the progress you've made so far and reapply. If you don't care about the finish, then don't bother, but it's something that would bother me if it were my own project.

I'd start with an 80 grit, bring it down to bare wood, then work my way up to at least a 220 if it's something my skin would be touching on the regular. Then, stain it the colour you want with a regular stain, finish it off with a spar varnish (if you're going to have any liquids on the desk, like your morning coffee), to prevent water damage in the future.