Hydraulic disc brake too loose
If the lever travel/bottoming problem got worse when you replaced your pads, that's a little unusual.

There is no way on these brakes to adjust the "bite point," otherwise known as lever travel. If it bottoms out or has excessive travel even with fresh pads, that's a symptom of air in the brake line, and the only solution is to bleed the brake.

The pink fluid is Tektro mineral oil. The brake leaking fluid is consistent with symptoms of air in the line. If the fluid leaked due to either the pistons being over-extended, the bleed port being open or loose, hose damage, or a loose hose fitting, it is probably correctable. If it's losing fluid anywhere else for no apparent reason, that's often indicative of a problem with the caliper seals that may not be fixable, since replacement seals for calipers often are not available. There's not really a middle ground situation of a small leak that still allows the brake to basically function. Any noticeable amount will quickly degrade brake function or get the pads contaminated.

At the very least it sounds like the brake needs to be bled. The basic Tektro bleed kit is cheap so it may be worth a shot. If it leaks oil after being bled, cut to the chase and get a whole new caliper or brake.