What should I say when asked for my expected CTC?
Give a number for the role rather than a percentage over your current salary. State the range you are targeting for that level, say it is based on the market for the scope of the role, and ask what band they have budgeted. If you name a multiple of your current package, you have anchored the whole negotiation to your previous employer's pay scale.
Should I accept a counter-offer from my current employer?
Decide it against the reason you started looking. If that reason was scope, technology or growth, money rarely resolves it and the same conversation returns within a year. If the reason was purely compensation and the counter genuinely closes the gap, accepting can be rational. Understand that a declined resignation usually changes how you are regarded in planning discussions.
How do I compare an offer with equity against one without?
Convert the equity into an annual figure using the vesting schedule, then discount it for risk. Listed-company stock has a market price and a clear schedule; private company equity depends on a future liquidity event and should be valued conservatively. Compare cash against cash first, then treat equity as the upside that separates two otherwise similar offers.
Is it risky to negotiate after receiving an offer letter?
A single professional counter, made once and with a reason attached to it, is normal and expected. Offers are almost never withdrawn over a reasonable counter. What does cause damage is repeated renegotiation after agreement, or using another offer as a threat rather than as information. Ask once, be specific about the component, and accept the answer.