Is it sinful to eat food whilst watching TV? Is it permissible to keep an indoor only cat (since birth) or must I try to give it outdoor time? Second question a person did lots of sin/kufr when he was depressed, then after medication got better- Is he accountable, should say shahada or just repent?

No, eating while the television is on is not a sin in itself, the ruling falls on what is being watched. There is no harm in keeping her indoors so long as you take care of her and do not neglect her, the woman in the hadith was punished for the neglect, not for the confining. Repenting is sufficient anything else is just waswas.