How do I know if a tat was done too deep or if it is infected?

Infection means swelling, redness, soreness, discharge, and then it progresses from there.

No real way to tell on the depth but perhaps it will be very uneven in shading but that would not be an infection issue.

Infection, there is always minor skin irritation and you can expect redness. The key is to keep it moist, with ointment for the first few days, and then lotion for a few weeks. It will be sore. If after a week you have blisters, swelling, a lot of pain, you need to see the doctor.

If the tattoo person uses clean needles and disinfects the skin prior to starting, and never laws the needles on the table, there should be no issue

Some people are sensitive to tattoos so that's not always the case as far as them being sterile and such. I know quite a few people who don't do well,one example a girl I know got a tatt on her foot and it swole up and exploded she had to have skin grafts
Also as far as to deep once it has been a while and you can feel the line work I'm pretty sure they went to deep. It is always best to investigate someone's work and skill before you allow them to scar you for life!

I am agree with you this depend on the skin .

I am agree with you this depend on the skin . If you have a sensitive skin your skin like redness, swell and also little bit warm .