The fun of the rules.
On ID, no you don't have to remove the current tag, just add your own just before slaughter (no point in doing it earlier) - in fact it is illegal to remove a mark under regulation 22 of PRIMO 2011 "No person may, unless authorised by the Secretary of State, remove or deface an identification mark.". Not sure the secretary of state will want a letter from you asking if it is ok !!
This is why it is generally better to buy weaners with just a temporary ID, as otherwise the abattoir has two tags to read (or tag and slapmark that differ) and match against one number on the paperwork. Not a real problem, but just tends to annoy the abattoir workers !
On your holding no. - yes I suspect that you would need to complete an AML2 to move the pigs between holdings even though the pig is not physically moving. You will also need to start a fresh movement book for the new holding no. and show the pig moving out of the old movement book. This does not by the way stop you taking it immediately to slaughter. It is a grey area as to whether it would prevent you selling (or giving it) live to anyone else for 20 days (ie moving it form your holding), as the law states the standstill applies to moving pigs between "premises", rather than between holding no.s , but unless you are planning this, would not worry about this.
Finally yes, you are right that standstills will not apply to your holding if you friend moves livestock, and visa versa, provding you load and unload directly on your holding ie drive to your holding and do not unload the animals on your fiends holding and walk them to yours. In the latter case you create a move onto your friends holding, and then he is on a standstill, and you cannot move your pigs onto your bit for 20 days. That's the rules, please understand that someone sat in an office in Brussels writes this stuff, which is then gold plated by someone in a similar Defra office. I suspect neither have visited a farm, or handled a pig.
Having said that we did have movement records in 1948, to quote from my Young Farmers Club Pig Keeping booklet "It is necessary to keep in ink or indelible pencil a records of all movements of pigs in a book that the local policeman may examine. This book must give the details of the date and place of purchase of all pigs bought in, and must also show the date and place of all sales."