Short answer to all that is yes.
Spoke tension should be even. IIRC Park tools say + or – 20%. Most people aim for closer to 10% and on a good day if you're patient you can get less than that. However, if you can feel loose spokes and tight spokes, they're out by a country mile.
It's not just a case of tightening the lose ones though as you need to try to keep the wheel round both side to side and up and down as well as keeping it in the centre line of the bike. By the way, the drive side on the rear should be a bit tighter as should the disc side on the front.
Either find a good wheel builder or have a look for some of the online guides and have a go yourself. It can be tricky but it's also very satisfying.
I find I can build more balanced wheels than I can buy but the truth is, I couldn't afford to pay a wheel builder to spend as long on them as I do!!!!