Premiere vs Roamio

With the sale Tivo has going right now for Tivo Roamio's I'm thinking of upgrading my Premiere Lifetime box (this is just the 2-tuner unit). Two questions:

Right now I use a Roku 3 for Netflix and Plex due to their speed over the Premiere. Netflix and Plex on the Roku take approx. 5-sec. to load while on the Premiere it takes nearly a minute for Netflix and 25-sec. for Plex. Both interfaces are pretty sluggish too.

Are the load times for either improved on the Roamio? How long does each take? I'm not expecting Roku speeds (Tivo is doing a lot more than Roku) but a minute is painfully slow. One of the big things for me is consolidating boxes.

If I decide to get the Roamio (basic unit, not Plus or Pro) I can still use the Mini, right? How many tuners does the Mini require?

I installed a much bigger drive in the Premiere. I assume if I transfer the drive into the Roamio I'll loose the saved shows, but the drive itself should be compatible, correct?

Finally, if I wanted to preserve the shows (I have a lot of saved programming for my kids) what would the best method be to do this?