If i buy an advance train ticket and miss my connecting train will i have to buy another ticket?

If you miss your connecting train because the first train arrives at Cardiff Central late than your advance ticket will be valid on the next available train and if you ask at the ticket office, they will endorse its validity for you.

You should be ok but the only thing is, that if you do miss your connection and you have to get a later train and you had booked seats you will not have booked seats on the later train.

As long as the one ticket covers the whole journey and missing the connection was not your own fault (e.g. it was because the first train arrived late, rather than because you went shopping and forgot the time of the connection) then your ticket remains valid, although it is wise to take this up with staff at the station where the problem occurs and get authorisation to travel on a later train, rather than just get on it. If you are using two separate tickets for one journey (i.e. one ticket from A to B & another from B to C, called 'ticket-splitting') and the second one is for a specific train, then if you miss the connection the railway company may well treat this as you simply missing the train (especially if it was another company's train which had been late) and so you might have to buy another ticket. This can make saving money by 'ticket-splitting' risky.

As long as you don't have any time restrictions on your ticket the answer is no, but if you have a "saver" ticket you may need to find if you will have to pay any penalties getting the next train. Normally i travel between Bedford and London, when i get a "saver" ticket I can only travel between 9:00 and 16:00 and then after that not till after 19:00 but I can get any train during this time. the same goes for "peak" tickets as long as you travel on the day you are supposed to it doesn't mater what time or which train to get.