Usually not, if it stays within permitted development. In broad terms: single storey, not in front of the house, and no more than half the land around the original house covered by buildings. Height is the one that catches people out — if any part of it sits within two metres of a boundary, the whole structure must be no more than 2.5 metres tall. Further from the boundary you can go higher. Listed buildings and conservation areas are treated differently. We'll check your specific site before designing anything.
Separately from planning, sometimes yes. As a rough guide, small outbuildings under 15 square metres internally with no sleeping accommodation are usually exempt; between 15 and 30 square metres they can still be exempt, depending on how close they are to a boundary and what they're built from. Anything with sleeping accommodation needs approval regardless of size. All electrical work must comply with Part P whatever the size of the building — we have electricians we work with who handle that side.
Yes to all of it. Home offices, gyms, studios and workshops are exactly what permitted development is designed for — the rules describe it as use “incidental to the enjoyment of the dwelling”. What you can't do without full planning permission is use it as self-contained living accommodation or as separate commercial premises. Insulation, power, lighting and heating are all straightforward to build in, and worth doing properly if you'll use it year-round.