Good Question

What are Top Down and Bottom Up compile methodologies in Synthesis?

In top down compile methodology you start compiling from the top of the design hierarchy. Whereas in the bottom up compile methodology we start building from the bottom of the design hierarcy. In general we go for the top down compile method.

Why should we not use tri-state logic arbitrarily?

Tri-state logic reduces testability
Tri-state logic is difficult to optimize - since it cannot be buffered leading to max fanout violations and heavily loaded nets

However tri-state logic can provide significant savings in area.