Most home winemakers use two types of fermentors, "a primary" and "a secondary". The primary is usually a bucket type vessel. It handles rapid ferments better, is easier to clean, is easier to manage fruit solids, and gives some exposure to oxygen. The secondary fermentor is usually a large bottle; it is suited for slower and finishing ferments. Oxygen exposure is limited in the secondary.
I start my wines in a primary and they will be in there for somewhere around 4-8 days depending on the wine, yeast, and temperature. When the SG gets around 1.020, I will rack it to the secondary to finish fermenting. Some fruits and their seeds can impart a bitter flavor to the wine if they are left in there too long. Letting your wine sit on the gross lees (the pile of sludge at the bottom of the bucket) for too long can also impart off flavors. Moving your wine to the secondary while it is still fermenting will put your wine under airlock and keep it safe for the last stages of the ferment.
Normally your recipe will start with campden tablets, so no, I wouldn't add more at this stage. You will need to add some (along with sorbate) if you plan to back sweeten the wine and you may want to add some if you plan to age the wine bulk or in bottle. If you're making a kit wine, the juice in the bag already has the campden ingredients in it for you.