I've answered to your email but I'm posting my reply here too in case other people wonder.

1. For now, the only way you can translate more than one sentence at a time is from the search. Type a word in the search bar, it will display results (provided you entered something in English or Japanese that is quite common). You can translate from the results. It displays 10 sentences per page but I can make it display more sentences per page if you feel this is a good solution for you to translate several sentences. Just let me know.

2. For now it's not possible yet. I mean, I probably could, but I have very little time (especially these days), and I'd rather set up some automated system for that.
Besides, we did consider giving the possibility to users to download a file with sentences formatted to be opened with a program called PoEdit. You will then have a page somewhere on Tatoeba where you can upload this file, and it will import your sentences. It's not likely to be implemented before end of January though.

Alright, we've added a "show more..." link in the random sentence. You can click on it to display more than one random sentence :)

You will be able to specify the language and the number of sentences displayed.