The immigration rules have specified who a dependant is as someone is a partner or child of the main applicant. Please note that the entry clearance as dependants, the child must be under th age of 18. Child dependants over the age of 18 may still qualify as dependants as long as they reached the age of 18 in the UK as child dpeendants of the main applicant.
If you are looking to come to the UK as a dependant of a Representative of an overseas business, you have to be over the age of 18 (with the exception of child dependants). As mentioned above, child dependants over the age of 18 may still be deemed as dependants if they have become over 18 in the UK.
Note also, that child dependants under this route would have to be at most 18 years old as at the time of entry into the UK. While other dependants must be over the age of 18 as at the date of entry clearance into the country.
Importantly, a child born to someone who is a dependant under this route can apply also as a dependant in the same aplication.
From 01-10-13, it became possible to switch into this category as a dependant of a sole representative (as the route used to be called). The only instances where switching under this category is not possible is where the applicant is currently in the country as a visitor or on temporary admission/release.
If your current visa in the UK is as a dependent of a representative of an overseas business, you should be able to renew your visa so long as you continue to meet the conditions and requirements of your current leave. Understand that your visa to the UK is on the basis of the main applicant, therefore, extension will be in line with the main applicant as well.
You should be able to apply for settlement (Indefinite leave to remain) when the sole rep is applying for his/hers. Importantly, you both should have been resident continuously and lawfully in the UK for a period of 5 years.