About the climbing 10-month-old child: The only practical advice I can offer is that you give her lots of distractions when she's in her playpen or stroller: toys, little books, anything that will keep her busy with non-climbing activity. But now that her ability and her urge to climb are so strong, there's not much more you can do; if you take her out of the playpen, there's a lot of other places where she'll try to climb, etc etc. This is a really tough time, but it should prepare you for the bigger challenge when she's walking (and running!!) on her own. Good luck!
Try expanding the baby's play area. Instead of confining her to a playpen, try confining her to a room. Child-proof(ha ha) the room and block the entrance(s) with a fence. Remove items the baby may get hurt on if she falls, i.e. coffee table, unpadded chairs, sharp objects/corners etc.. You can even purchase 3 or 4 of the little fences and connect them together to make an even bigger play area than her playpen. I do not know which brand of fences will allow you to connect them together but I'm pretty sure they exist.
Your little mountain climber may benefit from one of the many playsets on sale at your nearest Toys 'R' Us. They're made of plastic with rounded corners and provide lots of climbing fun. Some of them are not appropriate for infants. You may want to stop by and find out more info. The upside is most of them can be expanded by purchasing other pieces and they can accomodate children up to the age of about 7. The downside to these playsets is that they take up a lot of room.
When my daughter was at the climbing age, it was more economical for me to expand her play area. Also, I was an apartment dweller so space was another issue. My daughter escaped major injuries and is now a happy 12 year old.
Re: the stroller ... have you tried buying one of those halter-and-leash affairs, sometimes used for toddlers to keep them from running into the street -- only don't use the leash part... Just put the halter on the baby, and strap her into the stroller with that IN ADDITION to the regular straps. That should keep her from turning around.
Re: the playpen ... many people feel it is safer not to keep a climber in a playpen at all, for fear they'll fall over the top. I quit using the playpen when my daughter was less than a year old, for that reason. THe baby *gate* did not have a flat top ... so she really couldn't get enough purchase to get over the top of that. Two or three times she tried to climb the baby gate and I hid and watched her ... she got stuck, as I knew she would, and although it sounds unkind, I let her hang there and cry for 10 or 15 seconds before saving her. After that she became afraid of climbing the babygate, but persisted (to this day) in climbing absolutely everything else. (Falling never deters her at all, only feeling stuck.) Since I couldn't keep her in a playpen after about 10 months, I just took her everywhere with me. To the bathroom. In the bathtub. In the kitchen. Not much privacy, but at least she's safe.