We can only have 4 HG players. If we have 5 English players over the age of 21 in the squad one will take up 1 of the 17 foreign spots.
I have done by research on this and from what I can find we can have as many as 17 "Foreign" senior and however "Home Grown" senior players we want, so long as it is all within the 25 senior players quota. So I don't know where you are getting that information from.
City is not signing Dele Alli.
I can think of several reasons why we should sign him; firstly that we need a 4th AM if Pep is going to stick with having 2 AM's in a Starting XI, secondly we need another HG player to allow Delph to be sold/loaned and thirdly if we are going to be forced (though the squad rules set by the EPL/UEFA) to buy "Home Grown" players then we might as well get the best there is, players such as Alli.
Likewise from the perspective of Alli himself, where would you rather be, a club which potentially faces tough times ahead (and trophyless ones at that) or do you want to be in a club which has lots of ambition (and the potential/resources to achieve), is able to take on the likes Real Madrid, which would help you win every trophy there is and in turn make you a legend of the game?
In other words, it makes sense for both City and Alli for him to join our club.
The fact you think they would sell to us is bizarre.
If there is one thing you can say about Levy's Spurs team, it is that no player can be considered to be "unsellable", even if he demands a high price at the end of the day. Otherwise they would not have sold Walker to us, Bale and Modric to Real Madrid and both Carrick and Bebertov to United. Not that I have too much against Spurs (especially when compared to the Arsenal) but that is the reality of the situation, a situation City need to be very willing to exploit.
Pep likes small squads. Pep has typically had small squads. Pep has won the treble with small squads. I don't see an issue.
Pep had over 30 players on within his Treble winning 2008-2009 FCB Squad and his European Double winning 2010-2011 squad while at Bayen (Who won the Treble in 2012-2013 with around 27 players) he also had around 25-31 players in the 3 seasons he was at there (Where he won 2 Domestic Doubles as well as an additional League Title, a Club World Club and 3 UCL SF apperences to boot).
Considering how much tougher it is for a EPL club to win a European Treble (let alone a Quadruple) for any manager (even some of the best ones*), one would say that trying to doing it with 23-25 players (in fact you need at least 33-35 players, which the rules do not permit as things stand) is going to be very tough, trying to doing it with less players then that would be all but impossible since it is virtually impossible for a the same starting XI (as Chelsea showed in recent years) to play 50-60 games to the same high standard, no matter how good they are as players.
*For example Fergie won the Treble for United with over 30 players within his squad.