podcast app that can play downloaded podcasts trasferred from PC
As far as I know, there is no specific solution like that for podcasts.

If you have them as media files, you can of course upload them to a device and play using any multimedia program like VLC. The downside is that you will have to organize them yourself.

However, I really encourage you to try a podcast app like Podcast Addict. Most of these allow you to choose to stream or download the podcast, keep track of new episodes (you will get a notification on your device), search for new podcasts and much more :-)

In general, the biggest point-of-view change when coming from iOS will be the fact that your Android phone is much more autonomous than an iPhone :-) You are expected to do most stuff locally on the phone and it is most efficient that way :-)