Generally yes? Or an absolute unequivocal yes in every single top league, with only one single manager being good enough to buck that trend?
For your questions I'll give a Yes/No and also expand on why I feel that way.
A bit reductive to try and remove all context except the bit that suits you though, isnt it? Yes/No will suffice.
No.
I don't think it is at all reductive and I'll explain my "no" here by saying that I think the important context is that it is our current manager who has been the person that has created all of that context. It is largely because of Pochettino that we have managed to consistently punch above our weight for the last 4 years that has led to those increases in the stature of our club and the additional income that has brought (that he hasn't been lucky enough to get a decent portion of to actually spend). When he came in we hoped for a top 4 finish, we didn't ever actually expect one. He changed the expectations of the club.
Is it an absolute fact, our 6th biggest budget is increasing, and more rapidly than our rivals? Yes/No will suffice.
No.
It not a fact at all. Below are the facts:
Since Pochettino took over the club in 2014 our wage bill has grown by a grand total of £48 million. In that same time:
Liverpool have grown their wages by £120 million.
Man Utd grown theirs by £81 million.
Arsenal grown theirs by £57 million.
Emirates Marketing Project have added £55 million.
Chelsea have added £51 million.
So our sixth biggest budget is actually moving slightly further behind three of the clubs ahead of us and considerably further behind two of them.
Further to the above clubs that we have fallen further behind, the clubs below us have been catching us up:
Everton have increased their wage bill by £86 million in that same period that we increased ours by only £48 million.
Leicester increased theirs by £83 million.
Crystal Palace by £72 million.
and Southampton by £50 million.
Note that all of these figures are only the last set of published accounts, so there is of course the possibility that we have made very large increases in that last year (which is quite likely) while the other clubs have stood still (which is quite unlikely), that is all just speculation though and not fact.
The reality is that as of the last set of published accounts for all clubs our wage bill was closer to those of Brighton, Saudi Sportswashing Machine, Burnley, Watford, Swansea, West Brom, Stoke, Bournemouth, West Ham, Southampton, Crystal Palace, Leicester and Everton than it was to the next club up from us - Arsenal. Lord only knows how many more clubs would appear in that list if considering Chelsea, Liverpool, Man Utd or Emirates Marketing Project instead of Arsenal, but the reality is that our wage budget was closer to Huddersfield who had the lowest budget in the league than it was to Liverpool who had only the 4th biggest.
Our current squad, performing at an expected level - how many teams are better? Is it 5 or more? Yes/No will suffice.
No.
They are not performing at an expected level. I think this squad should be good enough to get 3rd in this league performing at its max, with 6th being the absolute worst place that it should finish in. However I think some of that ignores the fact that while the squad is good on paper, the team is weak in a couple of positions (RB and CM) we also have problems with some players wanting to go (Alderweireld, Eriksen, Rose) and also have had others injured (Lo Celso, Sessegnon, Foyth) or coming back from injury and out of form (Wanyama, Dier, Dele). Some of these problems are now fixing themselves, others need to be addressed by the manager (and perhaps will as the injured/out of form players return).
With just two key buys - by your specification - how many better teams than us would there be? Is it 5 or more? Yes/No will suffice.
Erm I'm not sure that one can be answered with a yes or no. It hugely depends on who the two buys are and also whether our rivals each go and sign 2 players as well. My thoughts here are that if we were to go out and buy a right back and defensive minded midfield player, both of comparable quality to NDombele and the other clubs stood still then we would definitely be right up there in the top 3 (although I think we would need to do the same with another centre half, left back and attacking midfield player to actually be considering winning the league.
I don't really understand this question though to be honest? I'm sure if Poch was given a good budget to go out and get two key players then our results and position would improve as a result anyway, especially as he could then jettison two of our weaker players in our team in Aurier and Winks/Sissoko and replace them with much better players.