1).Will it still count towards my B1 licence even though its unpaid?
AMC 66.A.10 states that the maintenance experience must be written up in a manner that the reader has a reasonable understanding of where, when and what maintenance constitutes the experience.
It does not matter if your paid or not. You'd have to record every job individually and a log book is ideal for this ( eg.
Association of Licensed Aircraft Engineers (ALAE) - ALAE log book information ) however if you do manage to get work experience they will probably have their own experience sheets for approvals etc and they would suffice and save you money.
2).Will I struggle to find an unpaid position?
The way the industry is going free labour might be appreciated. Try sending a letter and C.V to some of the companies who do heavy Maint. Some others on here might be able to help or know of a better way...
Best of luck