Light up garden and Summerhouse

Get yourself a registered electrician to advise. Too much info required to say anything of significance here... Good Luck, Carl.

With out the big blue book and some test equipment, it is impossible to know. Don’t worry about them being registered, it would only be minor works. You only need to worry about Competent Person Schemes for notifiable work, even then it’s only real benefit is in price and simplicity, it certainly isn't any safer.

You should seek a professional to guide you on thing project. There are certain things to consider when running power outside. For example. Rcd protection. Volt drop vs length of cable. Expected loads. Type of cable. Method of installation. Earthing arrangement. Testing etc. Unless you have a good knowledge of the above....best to asks someone who has the experience.

Totally agree with s l service and e l x electrical. People think they can do it themselves with no knowledge or experience