Here are answers to some of your questions (note that these are mainly my personal opinion):
2. DMZ - no, I don't suggest visiting with young children - very interesting for adults but can be boring for young children
3. Cultural music/dance shows:
NANTA - percussion performance, entertaining for both adults and children. To book from outside Korea see:
http://ticket.interpark.com/Global/Play/Goods/GoodsInfo.asp?GoodsCode=15010874or
http://ticket.interpark.com/Global/Play/Goods/GoodsInfo.asp?GoodsCode=15014878BIBAP is another non-verbal performance that may keep children's interest as well. See
http://ticket.interpark.com/Global/Play/Goods/GoodsInfo.asp?GoodsCode=140002234. See some other options that may be of interest to children here:
http://www.korea4expats.com/article-art-galleries-museums-children-Seoul-Gyeonggido.html5. The city tour bus should be fine regardless of the temperature. The buses are generally comfortable and heated. Depending on where you're going, you would likely not be outside that long either. The buses offer on/off options.
Suggest you post the wheelchair rental request on its own with "where to rent a wheelchair in Seoul' on the subject line.
Hope this helps and that you enjoy your stay in Seoul.