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Usually they will not give you the full value. Depending on how "safe" they deem the security, they might only allow you to borrow 50%-70% against it.

And most (probably all) of these forbid you from using the loan proceeds to buy more securities.

There is usually a margin requirement (25 to 75% depending on type of equity). And yes, you can.

No. You are not allowed to use these loans for investments, you would need a different type of loan for margin trading.