Can I reserve return tickets to a layover country and separately reserve return tickets from layover to my destination?

I agree with the other answers, you can definitely do it, but you need to be careful about short connections. Two hours is clearly not enough: it’s barely enough if everything goes according to plan, as you need to:

• exit the plane
• get to passport control, wait in line and go through immigration
• retrieve your bags and go through customs
• go to departures and find the relevant bag drop/check-in counter
• wait in line and drop your bags before the check-in deadline (often one hour before departure).

Four to six hours is the strict minimum, and even then, if your incoming flight is very late for whatever reason, you are on your own.

I would recommend you look into fares which allow a stopover (which is a special layover, usually over 24 hours, where you reclaim your bags and check them back in). In your case, you would have a stopover on the way in, but a regular layover on the way out.

Fares with stopovers are not always easy to find. Some airlines will be quite open about it, for others it’s nearly impossible to book them without a travel agent. Your best chance for a stopover is an airline which is based in the city where you need it, so Thai Airways is probably your best bet.

Sure it's allowed; I do that all the time.

Make sure you leave enough time between your 'connections' - if you miss your 'connection' because your incoming flight is late, it is your problem, not the airlines, so 4 - 6 hours should be your minimum 'connection' time.
You should be aware that you need to pick up your luggage, and check it in for the next flight- there will of course be no 'transfer'.

As others mentioned, depending on the countries and airlines, your plan can save you money or can turn out more expensive - make sure to check all variants (unless you are rich and don't care about the cost). Sometimes booking all one-way flights is the cheapest - because you can pick different airlines for each leg. Sometimes a multi-destination ticket is cheaper.

It is possible, provided that you get a visa as you describe. However, you might not want to book separate tickets like this.

There are a few ways to book this trip, and while all will "work," some may be substantially more expensive than others:

1. One multi-stop ticket (single purchase transaction) covering (SEA->BKK; BKK->DEL; DEL->SEA).
2. The same, except three separate tickets. SEA->BKK; BKK->DEL; DEL->SEA (as there are no direct flights from Seattle to Bangkok, you'll need to stop somewhere else on the way)
3. Two separate tickets. SEA->BKK and (BKK->DEL; DEL->SEA)
4. Two separate tickets, as you propose. (SEA->BKK; BKK->SEA) and (BKK->DEL; DEL->BKK)

The problem with booking separate tickets is that you, not the airline, are responsible for your own connection. If your flight is delayed, you could be responsible for the cost of rebooking, while with a single ticket, the airline is responsible for getting you there even if you miss your connection. You'll usually have to claim and recheck baggage, which can require passing through immigration and customs (which may require a multiple-entry visa). If baggage fees apply, you'll have to pay them again. Also, if you need to change your flights, you'll likely need to pay multiple change fees, as each ticket is separate.

And in this case, since there are no direct flights from Seattle to Bangkok, it's not clear that it makes logical sense to fly back through Bangkok for your return flight; there are many one-stop routings between Delhi and Seattle.

Particularly if you have checked baggage, I'd avoid #4, because you'll likely need to claim and recheck your bags during your return flight. If you do book separate tickets, I'd allow a long time between connecting flights to allow some margin for delays, and obtain a multiple-entry visa so you can enter the country on your return trip as well.

Finding good fares on multi-stop airline tickets is tricky (and sometimes impossible), and requires searching a lot of different combinations. You might consider working with a travel agent (or a service like Flightfox).