Yes. We do at least 3-4 times a month a long with playing at the local museum kids area a few times a month too.
No. I had joined this mom group...actuall 2 of them. The very first playdate we went to, no one introduced themselves or said hi to us, so that was the end of that. The other group I joined had lots of moms, but only like a group of moms would come all the time and they were really just not my cup of tea. I did make one friend out of it but we're not close or anything.