Refinancing conventional loan to an FHA

[Raymond Bas]

Hello, I am a 25 year old looking to invest in his first multifamily property. My intention is to house hack. I live in South Texas in the Rio Grande Valley. Most of the current listings in my area are four-plexes that are fully occupied, usually listing for $320k-$390k with rent being from $600-$1100 depending on the quality of the apt and the location. I have a couple of questions that I would greatly appreciate some insight on:

1) If the numbers were to work and I purchase a fully rented four-plex with a conventional loan, can I later refinance it into an FHA loan if one of the tenants were to move out and I move in? Of course this would mean that I will still be paying my own rent ($600/month) at my current apt while the property is full rented.

2) With a conventional loan I am aware that the down payment will likely be higher up to 20%. From my studying, dropping nearly $70k for a property is not necessarily a good move, so what would be best in this situation? 

This is my first post on the bigger pockets forum and I am excited to hear from many of you. Thank you!