Yes absolutely - and you’ll be paying a premium as it’s been a second home.
Yes absolutely - in fact if you’re staying until October 2019 you’re French tax residents and need to, as an initial step, affiliate to the health system. You will be required to submit tax returns in Spring 2020 relating to your worldwide income.
Just out of interest - are you saying you’ve never paid any Taxe d’Hab since buying your second home in France?
Technically, after being here 3 months, with the intention to stay, you need to affiliate to the health system via whatever appropriate route. Importantly it’s not a ‘number of days’ game - your French residency will be an unambiguous matter of fact.