Reddit mentions of Lamy T10 Black Ink

No problems!

Fountain pens can be filled by a number of ways. Cartridges are "bullets" of pre-filled ink which you simply insert into the pen, and swap out for a new one when it runs empty (see here). Converters, on the other hand, looks very similar and functions as a cartridge. However, it comes empty, you have to fill it up yourself (with ink purchased separately), and refill it when it runs empty. The advantage of this is that you can use your own preferred ink, since cartridges are pre-filled and you might not like the supplied colour, consistency etc (see here). Pistons are what's seen in higher end pens, like the Montblancs and Pelikans, where you simply dip the pen tip into the ink well and turn a piston (located on the barrel) to suck up the ink into the pen. The advantage of this is the capacity is much, much larger than cartridges or converters (from my eyeballing, at least 5 or 6 times larger). There're also other methods of filling such as rubber sacs and eyedroppers, but they're usually found in vintage pens and are much rarer in pens made today.

Left handedness shouldn't affect your fountain pen usage, especially with a stock (i.e. out of the box) nib which comes with a Lamy Safari. The nib tip in this case is round, so essentially the same shape as a rollerball. It'll be able to write in any direction and feel the same way in each direction. The difference is that ink may take a little longer to dry and you want to avoid smudging it, but since you're lefthanded you're probably aware of this already. The issue of lefthandedness only comes in if you want to customise your nib tip - in that case, the direction of writing can result in a lot of interesting results (see here for examples). However, as a beginner, a standard nib will not be affected by handedness.

Ok thanks. How long should it take to dry? In a science exam I will need to turn the page very quickly so I can't really wait for long. I ordered the pen to write faster and not get cramp so that could be an issue.
This is the ink I ordered https://www.amazon.co.uk/gp/product/B003VW13ZU/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1