Stake Clerk and Stake Executive Secretary have access to a web based custom reports section. I'm an assistant so I'm not sure what the options are there (It'd be nice to have access though - I already submitted feedback), but there are other ways to accomplish some of those reports.
For unbaptized members, you could:
- In LCR, go to Reports > Unit Statistics
- Scroll down to "Members of Record Age 9 or Older" (it's the last line at the moment)
- Click on the number under the ward you want to look at
- A member list of those members will be generated that you can print
I'm not sure about part member families. I'm in a YSA stake so I can't test that. Other lists of members can be generated from that same Unit Statistics page, such as converts, recommend status, single adults, etc.