Visiting India - what amount of cash is recommended, and in which currency?

You probably won't be able to take rupees - currency controls, at least on paper, prohibit non-residents bringing rupees into India, which means it's also difficult to change local currency into rupees outside of India. (See also this question.)

I would strongly recommend converting to rupees rather than trying to use dollars. You are unlikely to have any trouble exchanging US dollar bills - your hotel will probably do it, if you want a simple life, but there are plenty of options. This question is quite helpful. Taking money out from the (airport?) ATMs rather than bringing in notes may also be a good way to convert cash, though there may be all sorts of interesting charges from your bank.

(I didn't pay for anything on a credit card while in India so I can't speak as to how widely accepted they are.)

The regulations were changed in January 2015 to allow any persons other than from Pakistan and Bangladesh to bring in or take out upto 25,000 Rs, even if not resident of india. See: http://www.cbec.gov.in/resources//htdocs-cbec/customs/cs-circulars/cs-circulars-2015/circ03-2015cs.pdf

I would advice carrying some small of indian money say upto 7000 Rupees which is not a problem, just in case you need some urgency before finding an exchange, but there should be exchanges in the airport.

And generally if you are living in and around Delhi,its shouldn't be problem to pay with your creditcards for dinners i mean in good hotels,but not Taxis i hope.But i would recommend you to convert some dollars and have around 10k always with you,so bring on some dollars and get converted here.

Always try to pay money in indian currency whenever possible.

Daily expenses would differ based on what your choices may be around 10k+ for a normal living

Most taxis and almost all big restaurants take credit-cards, and all ATMs take foreign debit-cards.

I spend less than 10,000 INR a week in cash when I go to India.

You can bring dollars with you (as it is very difficult to bring Indian currency from outside). Then, you can go to banks for exchanging foreign currency.

"should I take US Dollar or Indian Rupees?"

Make sure you obtain notes of 100 and 500 as after the demonetization, it is very difficult to get change for ? 2000 note

And how much will I need estimated per day?

It totally depends on where you will be going and how exactly you will spend your day. On a normal day with average shopping, and eating food outside, you could spend between INR 2000 to 5000. On a busy day, with lots of travel in Delhi, and visiting shopping malls, you might end up spending between 10,000-20,000.

In other words, what's the chance to pay dinner or taxis with credit card?

If you are in Delhi, you can pay with credit cards at food outlets (Domino's,Subway, KFC, etc.). But to buy anything from local vendors, thrift shops, and for travel, always keep change in small denominations.

Hope, this helps :)