Does mead fermentation time depend on the amount you're brewing? Such as will a mead batch of 100 Litres take longer to brew than 10 Litres?

There should be no difference. Do a large batch so that you will still have mead to drink while waiting for your next batch to "drop clear". I won't bottle until the mead has sat in the carboy (secondary) for a year.

Mead Fermentation Time

Fermentation time should be 1-2 weeks regardless of batch size if you pitch a proper amount of viable yeast and supply them with the initial oxygen and nutrients they need. Most people starting off have no clue what those words even mean and their fermentations take a long time, get stuck and turn out poorly.

Pitching rates are based on specific gravity and volume. Go to MRMALTY for a good free calculator.