1. Edinburgh to London will use 1 travel day and 1 inbound/outbound day. London to Paris will use another travel day and another inbound/outbound day. You won’t have any inbound/outbound days left.
2. For Eurostar you can't. For the Bernina express you can, but you will then also need to pay the difference between the regular 1st ad 2nd class fares, which won't be cheap. You'd then better buy a 1st class pass to begin with.

There is no 7pm rule anymore. The day you board the train is what matters. On your example you'll use 2 pass days + 2 inbound/outbound days so you'll have to buy tickets to get back to the UK.

If you have an Indian passport it's better to buy a Eurail pass (same price) so you don't have such limitation.

Otherwise buy a separate Edinburgh - London ticket, it's probably the cheapest journey.

No, you can't book 1st class reservations. It's possible to buy an upgrade in Switzerland but it'll be expensive. Cheaper to buy a 1st class pass in the first place.

Actually for the Bernina Express : I recommend not buying reservations for the panorama carriages, they're always loud and full with tour groups. For a better experience board the reservation-free regular carriages at the front or the hourly regional trains along the same route -> less busy, pull-down windows :)

As others have said, it’s the time of departure, Central European Time that counts. So the 1958 train on 17/05 will use a day, and the Eurostar (and other trains) on the 18/05 will use another day.

One way around this is to use the sleeper train, which departs Edinburgh at 2340 local time (0040 on the 18th CET). But you’d have to pay for a cabin unless you want to sit in a seat all night. And it doesn’t arrive in time for the 0630 for Paris. There are also a few bugs with adding this to your trip planner.

For first class upgrades, you can upgrade on LNER trains between Edinburgh and London (but not on Lumo, which operates the 1958) - either by bidding with Seatfrog, or by paying for ‘Weekend First’, which is offered onboard most off-peak trains (not just at the weekend).

If you buy a Eurail pass with your non European passport, then you don't need to bother about the outbound/inbound travel days in the UK.

Thanks all for your helpful replies.

I have few follow-ups question.

1. Considering I am going with Interrail Global pass - does this pass allows 2 inbounds as in my case? Got confused with this Travel in your own country | Interrail.eu as here only 1 inbound and 1 outbound mentioned. Kindly clarify. 
2.   @thibcabe and @AnnaB ,  I was going thru Article 5.6 of Booking Condition Booking Conditions | Interrail.eu and got confused.

 In case the country where you live and/or work -your official country of residence- is different than the nationality in your passport or legal equivalent, the country where you actually live and/or work prevails and should be indicated when ordering the Pass.  

Am I still eligible for EURail Global Pass. I hold Indian passport and works in UK with UK BRP.

TIA

Regards

1. With Interrail, you can travel in your country of residence on 2 of your travel days. It doesn't matter in which direction.
2. It looks like they're rephrased the conditions a bit. On the other hand, nobody will question your Eurail pass if you have an Indian passport.