Say for example I run an ecommerce website which mandates users to have a minimum balance of 1 bitcoin in their wallets to access the platform. In the event the balance in his wallet falls below 1 bitcoin he should not be able to access the platform and he should see a message on his screen saying "Please load to minimum balance".
So, the question is, can I, or the Bitcoin wallet provider I use, read the bitcoin balance of the users so as to fulfil the above business requirement?
All Bitcoin transactions are publicly available. This is fundamentally why Bitcoin can work as a truly decentralized currency. Bitcoin is different from the traditional banking system specifically because anybody can see and validate everyone's transactions. If only a few could access the information about people's balance, then it wouldn't be fully decentralized, it would be just like traditional banking.
So yes, you can calculate the balance of any Bitcoin address in the network.
The service provider can know the balance of the wallet, if the wallet is "hosted" one.
The service provider must know all the addresses associated with the wallet (this is pretty much the definition of a Bitcoin wallet in the first place). However, you do not need to know private keys needed to send out Bitcoins from the wallet, you can have "read-only" knowledge about the wallet.
However from your service it sounds like you are already using hosted wallets, so finding out the balance of the wallet should be just summing up unspent balance on the public addresses of the user wallet.
I think there is some general confusion as to what a wallet is, and how you interface with one. I'll try to be detailed but not too nitty-gritty.
A wallet is really two connected things. First it is a collection of private/public keypairs. In the case of standard addresses (P2PKH) each public/private keypair matches to 2 distinct Bitcoin addresses. This is because you can derive two addresses from the keypair because there is a compressed and uncompressed representation.
In the case of multi-signature the address is constructed based on all of the public keys involved in the transaction. This can create many addresses that represent the same keypairs or combinations thereof.
Based on the comment above you want to run a site that does 2ofN multisignature. Which means you control one of the keys at least, this means that your wallet is a collection of addresses that you have partial control of. At any time you can sum the balance of every address you mutually control with the user and come up with a total balance.
So, the answer is yes, you can contact the user when the balance falls below a certain amount since you have total knowledge of all keys that the user is using since you are party to them. This lets you compute based on the public ledgers information. This is also true for HD wallets / Keys so long as you compute a collection of multisig addresses derived from the HD keys.
