Annotations!
1A - double def.
3A - gueSTS I DUNno, reversed
7A - SET + UP
8A - PIE containing IX
9A - (WHIZ TROLLS)*
12A - HE within THOU ("you way back") within ONES*
16A - SHIN + Y[ou]
18A - /you view/ + L[esson] A[ctually]
19A - SWEET ("like honey") + IE
20A - palindrome
1D - [serve]D + IS + H
2D - TIRADE* + T
3D - PLANE*
4D - DEATH with the A changed to P[iety]
5D - /sics/
6D - S[preading] + NEE + Z[ygomatic] E[czema]
10D - [he]R [escap]E [wa]S + CUE + D[aring]
11D - &lit, SHOES* containing [thei]R
13D - E[lvis] G[oes] Y[eah] P[raising] T[ennessee]
14D - O + FUSE
15D - double def.
17D - prehistorIC Eras