Paranoid for sure and the kind of family that does better with a Nanny in their home with their things. But a lot of the issues are normal first time parents to daycare in that they don't realize that it is "normal" for kids to nap in playpens - even though on the label for the playpen it will say not for sleeping. She is concerned about germs, child eating stuff, whatever. I actually do use a playpen or the exersaucer outside for those not moving around much since it keeps them out of the way of balls and runners.
Watch for further developmental delays in the child in the sense that the poor head and trunk control may also translate into feeding with poor chewing and swallowing issues.
For the blender do whatever you want and then take the food out and spread on a plate. Use a fork to "check" for pieces that are too big and either mash or remove. Tell the mom that that is what you do. Also as you feed you can do the same thing in the sense of mash larger pieces as you go just in case. And for this baby I would be very careful of pieces since child may not have good gag reflexes. Make sure that all foods are moist - applesauce is great as is yogurt or any jar of commercial first stage food. My special needs daughter still gags on anything dry. Even cereal softened in milk is not lubricated enough and needs sauce with it.
If you have a comfortor - the puffier the better lay that down on the floor for the baby to lay on and roll around - a play yard system might be a good investment depending on the age and play level of your other kids so the baby isnt' always the one that has to be up out of the way in something. Hopefully it is just a lack of practice on the part of the child but barely sitting at 9 months is certainly something to watch for. There is a support pillow you can get that baby sort of sits in and it helps support the trunk and provides padding when they fall backwards. Discourage the pillows behind the child due to rolling and suffocating if child is that delayed in movement. The comfortor will provide enough padding considering the child isn't falling down but sort of flopping down from only a foot off the ground.
For sleeping suit yourself on the crib issue but it is normal for kids to nap in playpens and if that is what you want to do then stand your ground on that one but let the family know how often and how you will be monitoring the child while they are sleeping. Not standing ground here means come next family if they want crib too are you going to get a second one or tell them no or hope the first child is out of the crib and then at what point does the crib become old and not meet safety standards - lots to think about before saying yes or no.
You also mentioned I believe that it was for a short time frame and fit with your current plans so you might just want to go along with whatever you can for that time while at the same time coaching the parents to what is normal.