Can a person with kidney problems drink tea?

Yes. Should probably avoid excessive tea drinking because there were some old reports about possible association of kidney stones i british troops stationed in india in days of the british empire. Probably had more to do with heat and inadequate hydration. Couple of cups or glasses/day in presence of kidney problems should be perfectly safe. Unless subject is fluid restricted for azotemia or dialysis.
Yes. If you mean the regular black tea then yes. This may be limited if you have fluid intake restrictions there are certain herbal teas which have a harmful "food substance" like in certain types of chinese herbal tea which can damage the kidney, ask your doctor.