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1 Across, Backed son getting into Cambridge University - blatant Favouritism (8)

5 Across, Be prudent and invest money in shares (6_

8 Across, Tree was chopped up to keep central parts of stove hot? (8)

10 Across, Meryl Streep's second to play Eugenia perhaps (6)

Compiler - KLINGSOR

Many Thanks

10 Myrtle, Eugenia - anagram of Meryl and the T, second letter, of Streep.

10 MYRTLE Eugenia is a genus of myrtles; anagram MERYL sTreep

1a NEPOTISM - favouritism
MIT (thanks to google) is a university in Cambridge (USA) !
s - son in MIT + open (blatant) reversed.

5 SCRIMP - be prudent
Again, thanks to google, Scrip is here : a provisional certificate of money subscribed to a bank or company, entitling the holder to a formal certificate and dividends.

m - money in scrip
If I were attempting this crossword, I think I would have given up by now

8a the clue should read: Tree WE'D chopped up to keep central parts of stove hot ?

Another site has given: Firewood (&lit)

tree : fir
we'd anagram
central parts of stOve hOt

&lit: firewood would keep the central parts of a stove hot.

correction: &lit

a tree we'd chopped up would keep the central parts of a stove hot.