From my understanding of your situation …. I hope this helps answer your questions:
(1) No. The SC does not have a right to enter your Lot or your EU unless one of the following [s122] provisions apply. Your consent is required if the entry is not an emergency, or unless there is an Order from the Tribunal.
Power of owners corporation to enter property in order to carry out work
122 Power of owners corporation to enter property in order to carry out work
(1) An owners corporation for a strata scheme may, by its agents, employees or contractors, enter on any part of the parcel of the scheme for the purpose of carrying out the following work:
(a) work required or authorised to be carried out by the owners corporation in accordance with this Act (including work relating to window safety devices and rectification work carried out under Part 11),
(b) work required to be carried out by the owners corporation by a notice given to it by a public authority,
(c) work required or authorised to be carried out by the owners corporation by an order under this Act.
(2) An owners corporation for a strata scheme may, by its agents, employees or contractors, enter on any part of the parcel for the purpose of determining whether any work is required to be carried out by the owners corporation in accordance with this Act.
(3) In an emergency, the owners corporation may enter any part of the parcel for those purposes at any time.
(4) In a case that is not an emergency, the owners corporation may enter any part of the parcel for those purposes with the consent of any occupier of that part of the parcel or, if the occupier does not consent, in accordance with an order of the Tribunal under this Division.
(5) A person must not obstruct or hinder an owners corporation in the exercise of its functions under this section.
Maximum penalty: 5 penalty units.
(6) An owners corporation is liable for any damage to a lot or any of its contents caused by or arising out of the carrying out of any work, or the exercise of a power of entry, referred to in this section unless the damage arose because the owners corporation was obstructed or hindered.
(2) No. Unless access is required by the Fire Authority or EPA etc. Proof by way of Notice should be supplied by the SC if access is required. You appear to have a Fire Egress Path on part of your EU. Has your strata scheme had a recent Fire Safety Audit – is that why the SC has become concerned about the egress path? Was a ‘defect’ found at your property that required rectification? A Fire Safety Inspection Audit may require that you trim your vegetation to allow a safe path for egress from the building to remedy any defects but your SC would probably be notified of this via the Inspection, then the SC would notify you.
Access for fire safety inspections
123 Access for fire safety inspections
(1) A person authorised to carry out an inspection under the Environmental Planning and Assessment Act 1979 of a building or premises that is part of a strata scheme for purposes relating to fire safety may give a written notice to the owners corporation requiring the owners corporation to ensure that access is provided, within a period or at a time specified in the notice, to the common property of the strata scheme and, if so specified, some or all of the lots in the strata scheme.
(2) An owners corporation must comply with a requirement of a notice given to the owners corporation under this section.
Maximum penalty: 20 penalty units.
(3) It is a defence to a prosecution for an offence against this section consisting of a failure to ensure that access is provided to a lot in a strata scheme if the owners corporation establishes that the owner or occupier of the lot refused to allow the access or could not be contacted by the owners corporation.
(3) I would not think that an individual SC member can be banned from entering a property. Should you feel intimidated by a particular person on the SC then you could request that when the SC enter your property on legitimate grounds and with the required notice under [s122] or [s123] that at least 2 members of the SC be present at all times.