Upvote:1
For the date of arrival and departure, I would enter the dates your flights will arrive and depart. They are almost certainly either the same day, or one day apart.
For whether you have a valid visa or residence permit, consider why the UK asks for certain information. They want to be satisfied that you are able to enter the country you are travelling from, in the unlikely event that they must refuse you entry and return you to that country. For this, they ask about whether you are a resident of that country.
If you have an I-797A with attached I-94, or I-797B, then you are approved to live and work in the US, but must also obtain a US visa (in this case H-1B) to actually travel there. You will return to India for visa stamping, then at some point in the future, back to the US.
To answer the question about your valid residence permit, I would enter your A number. This is the number tied to all of your US immigration, employment authorization, etc. This is the USCIS A# on your I-797, and on your EAD. Because these show you are authorized to live and work in the US, using the A number should be sufficient here. And UK visa officers are already familiar with the A number.