7 days in Iceland. Do I have enough time for my itinerary?

3 days is reasonable minimum (sporting endeavours aside) for Landmannlaugar to Thorsmork only. Thorsmork to Skogar you may or may not be able to walk given the volcanic situation. You can take advantage of bus timings to save days: your bus to L will get you there about lunchtime, and you have long daylight hours, so you can actually do quite a lot of walk the same day you arrive at L, though that means less time to enjoy the environment of L (weather permitting). Also, there is a bus out of Thorsmork at 4pm, so you can plan it, if careful, not to need to stay the night in Th, but again you lose the enjoyment of spending time there. Walking Thorsmork to Skogar, if it turns out possible, is typically a 12-14 hour walk, which in most cases is too long to get the 4pm bus out of Skogar, unless you split it as a 2-day walk.

In fact is it possible to do the Golden Circle and Blue Lagoon in the same day?

Theoretically, if you had a hire car and didn't mind that you only spent a brief time at each site, you probably could. But it doesn't make much sense. BL is near the airport, opposite side of R to GC, so makes sense to combine BL with an arrival/departure if flight times permit.

I suggest it makes more sense to set off to do the trek immediately on arrival. Then use what you have left over for what you can do with that. You know that golden circle takes a day. But treks have less certain timings, because weather and volcanoes happen.