One cause of protein slicks can be the protein from fish food. One way to clean the slicks more quickly can be to simply float a paper towel on the surface for a moment and then remove it and you can repeat this a few times. Sometimes the slicks are one of the symptoms of overfeeding. It can be ok to feed your fish multiple times a day but the amount would have to be truly tiny. I feed my fish once a day and only an amount they can eat within 2 to 3 minutes. It's important to remember that their stomach may be about the size of their eye and that it is quite normal in nature for them to find food only rarely.
Agree with the other good advice Laura and the other members have been sharing, you have many of the typical problems that happen to beginners. If you just stick with things and keep inquiring and learning, all these things will gradually clear up for you.
Take a look in second section, the tank startup section, of the Beginners Resource Center up above for some good articles about filters, filter maintenance and tank maintenance. The weekly gravel-clean-water-change is the most important and basic tank maintenance habit. Correct technique with fitler cleaning is also important though. As mentioned, the filter media needs to be gently squeezed or swished in tank water (not tap water) during one of your weekly maintenance procedures. The beneficial bacteria live in biofilms that remain tightly bound to the sponges and other media and will not wash away during the squeeze-out of the organic debris. If the filter has a fine floss pad to catch the smallest particles this can be squeezed out too, often lasting a month or two before needing replacement. The main sponge should last for years and any ceramic pre-fitler material even longer than that.
It is extremely difficult to maintain an algae free tank that receives direct sunlight. Most of the time aquarists will seek a way (curtain, solid background, etc.) to block direct sunlight and try to use the more controllable tank lighting that can be on a timer. The shortest photoperiod (period of hours with light on) that is of use to aquarium plants is 4 hours. Most beginner tanks should be run with lighting on somewhere between 4 and 8 hours based on multi-month experiments to figure out the best compromise between keeping algae at bay and having good plant growth. A 15 watt tube on a 10 gallon would put you nicely within the lighting range for low-light technique with your plants.
Yes, the weekly water change is the time to do other cleanings, like rocks and plants (plants must be done very gently.)
~~waterdrop~~