History:
I have been in the trade for 10 years.I have done a varied number of different electrical jobs from changing light switches, electric vehicle charge points to full rewires
Other:
Logic Certification Domestic Electrical Installer
Level 3 Award in the Requirements for Electrical Installations BS7671:2008(2015)
Level 3 Certificate in the Building Regulations for Electrical Installations in Dwellings
Level 2 Certificate in Fundamental Inspection,Testing and Initial Verification
18th edition IET wiring regulations level 3 qualified
City and Guilds 2919 EV Charge point installation
Answers:
No your fusebox does not need replacing it would only need replacing if you do not have enough space in it if you need to put a totally new circuit in it.
If you want it to the latest 18th edition regulations and it is currently a plastic consumer unit then replace it but you can not be forced to change it all new consumer units are metal if everything in it is working fine then i would not change it.
Depends how many mcbs in it and what brand it is also if any wires need extending i would say about £650 maximum cant give an exact price as i have not seen the job.
You would be looking at about £100 including a weatherproof socket
No you can not do it yourself you need a qualified electrician to do it