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Definitely get her a friend. They are social animals and need to always be kept in pairs. Make sure you check the sexes of both piggies yourself to ensure you are getting two females. Sorry to say, if they didn’t tell something as important as they must be kept in pairs, I wouldn’t rely on them giving you the correct information on their sex.
Make sure when you get her a friend that you bond them properly - this needs to be done on neutral territory. You can’t just put a new piggy straight in her cage. They need to be in a neutral bonding pen for several hours while they go through acceptance, you clean down the cage and then move them to the cage if all goes well in the bonding pen.
The guide explains the full process.
Bonding and Interaction: Illustrated social behaviours and bonding dynamics
Also make sure the cage is big enough for two. For two females it is a minimum of 120x60cm but 150x60cm is better.
In terms of her begging - she is training you to give into her! It’s what they do!
What enrichment does she have in her cage (even more important during the time she is alone)?
Something like not using bowls and instead throwing the veg and pellets onto a big pile of hay will allow her to use her brain and forage for them rather than it just being a case of sitting at a bowl which takes no thought.
Enrichment Ideas for Guinea Pigs
Fleece is not recommended over any other type bedding - bedding is a personal preference and you can use whichever works for you.
Make sure any disposable bedding and the hay are dust extracted though.
I use disposable beddings (I’ve tried many over the years!) and then top them with hay.