1. You can't change within the UK to tier 2 general. You also have to serve the cooling off period unless a sponsor is offering you a salary of £159,600 per annum, as clearly stated in the immigration rules.
uk-tier-2-employer-sponsored-visas/swit ... 88997.html
https://www.gov.uk/guidance/immigration ... sed-system
(c) An applicant who has, or was last granted leave as a Tier 2 (Intra-Company Transfer) Migrant must:
(i) have previously had leave as a Tier 2 (Intra-Company Transfer) Migrant under the Rules in place before 6 April 2010, or in the Established Staff sub-category under the Rules in place before 6 April 2011,
(ii) not have been granted entry clearance in this or any other route since the grant of leave referred to in (i) above; and
(iii) not be applying to work for the same Sponsor as sponsored him when he was last granted leave.
(k) Except where the period of engagement recorded by the Certificate of Sponsorship used in support of such entry clearance or leave to remain was three months or less, the applicant must not have had entry clearance or leave to remain as a Tier 2 Migrant at any time during the 12 months immediately before the date of the application, unless:
(i) the applicant’s last grant of leave was as a Tier 2 Migrant,
(ii) the applicant was not in the UK with leave as a Tier 2 Migrant during this period, and provides evidence to show this, or
(iii) the applicant will be paid a gross annual salary (as recorded by the Certificate of Sponsorship Checking Service entry, and including such allowances as are specified as acceptable for this purpose in paragraph 79 of Appendix A) of £159,600 per year or higher.
2. You can apply etc but you cannot be sponsored without serving the cooling off period unless the above applies.
3. Yes. You will need a new CoS and likely RLMT. You cannot work for ANY other company on your current visa.
There is a lot of conflicting information out there,
Not really, the immigration rules are very clear.