If you are making a change prior to departure of the 1st sector then most (all?) fares require repricing at the fares in effect at the time of the change

As far as change fees go, it depends on what the fare rules are. It would seem that you have a special unpublished fare from the travel agent which is why it states BT on the fare rather than a price. If there is a date change fee on this ticket then you will need to pay it; that a previous ticket may have had a "1st change free" rule is immaterial

If the agent hasn't checked the ticket rules and is just giving you the standard information, it is possible that the ticket does not have a date change fee; to find out what it is ( if there is one ) you need to ask your travel agent