1. The supplied cables do not have 'issues' as such but they are perhaps best viewed as being 'get you going' cables because they are obviously made to a price point. More expensive cables have better shielding and better BNC connectors with more reliable connection to the cables. However, plenty of people just use the supplied cables.
2. The best price/performance is something where I have a vested interest so I will leave that to others to help you.
3. Most people seem to use the AudioQuest jack to RCA convertor and then RCA to BNC convertors like below. These are widely available from Amazon and other online retailers for not much money.
Regarding where to buy Belden or other cable like the one you mention (there are many similar RG6 cables) it really depends on where you live. The cable cost is only between £1.50 and £2.50 /m so the postage will be a big factor in cost. Just look up suppliers local to you. Yes, get 75 ohm cables and BNC connectors.