I can't speak to Halloween, it's not a holiday I'm familiar with. I'm sure someone will turn up to deal with that aspect of the question.

On Christmas, let me point you to a much older threads: [This one](This one https://www.reddit.com/r/AskHistorians/comments/1t7hbg/what_are_the_historic_facts_about_december_25th/), in which I discuss some of the dating for 'earliest mention of Christmas' as well as the reason for the date. /u/Gadarn also gives some account of the reasons, and problems, of discussing appropriation of the holiday.

One of the issues, though, is not so much the date, but general customs. In varying European contexts, over hundreds of years, where Christianity is growing and becoming a default, or state-backed, religion, one would naturally expect that various local customs associated with festivals around the same time, e.g. Saturnalia, Yule, etc., would be incorporated by people into their 'Christmas' celebrations. There's little evidence that this was a deliberate 'Church strategy' though. By little, I mean none.

On Easter, the origins of the holiday are very clear. The Jewish Passover was well established as a feast. Early Christians held universally that Jesus died and rose again at Passover, and appear to start celebrating some type of Christian Pascha at least in the 2nd century. Melito of Sardis' On Pashcha appears as a very early corroboration of this. While probably first celebrated as a single, one-night event on 14th Nisan according to the Jewish calendar, it appears to have spread, and developed into the 3-day holiday more familiar today. Different dating practices lead to the Quartodeciman controversy, in which those groups that celebrated on 14th Nisan whatever day of the week it happened to be were told by other major church centres to conform to the (Roman, among others) practice of celebrating on the Sunday that followed 14th Nisan. This debate appears as early as the 2nd century and doesn't resolve until at least the 4h century.

There's zero evidence that Easter, as such, began as a pagan holiday. Did it, like Christmas, gain practices more commonly associated with generalised spring festivities? One would have every reason to think so.