No these part of the regs dont apply to fire safety.
Yes they do. The quoted paragraph 8 "Signs requiring some form of power must be provided with a guaranteed emergency supply in the event of a power cut, unless the hazard has thereby been eliminated." is taken from Part I of Schedule 1 to the Regs. The title of Schedule 1 says it relates to Regs 4 (4) and (5).
Reg 4 (4) says "Where this paragraph applies, the employer shall ... (a) in accordance with the requirements set out in Parts I to VII of Schedule
1, provide and maintain any appropriate safety sign (other than a hand signal or verbal communication) described in those Parts, or ensure such
sign is in place;"
Reg 4 (3) makes it clear that this paragraph applies to fire safety signs: "Without prejudice to paragraph (1), sub-paragraphs (a) and (b) of
paragraph (4) shall also apply in relation to fire safety signs where they are required to comply with the provisions of any enactment (whether in an Act or instrument)."
Regulation 2 defines "fire safety sign":
“fire safety sign” means a sign (including an illuminated sign or an acoustic signal)
which –
(i) provides information on escape routes and emergency exits in case of fire;
(ii) provides information on the identification or location of fire-fighting equipment; or
(iii) gives warning in case of fire;