So I shoot scenes with my cellphone (whether FHD or UHD). But other scenes I take them from clips I find online in a subscription service. If I try to make the video of contiguous scenes combining from phone and the other clips it is easily observed they are different, there is no continuity on light/color. Which filters or steps do I need to make so it appears to have continuity?
For future videos, you better have a defined reference in all videos. For example a clapperboard or a standardized grey card. Then you can match all videos during colour grading both regarding the white balance and exposure. Usually editors let you set the black and white point or midtone with a colour picking tool that you use on the clapperboard or greycard. Or you mask out a grey area and using diagrams to adjust colours until the red/green/blue values are equal.
For existing videos without such reference and especially for videos from external sources you need more guess work but you should get there close enough.
Anyway, you need a video editor that helps with colour grading. The steps depend on your editor. Some of them offer graphs or diagrams which help for comparison between clips. Usually there's also a copy&paste function, so that you can use the same colour settings for multiple clips. Some even have automatic functions, that may or may not be useful. For example Adobe's Premiere Pro (and here is mini-tutorial on the topic). Adobe offers a free trial, so you can check if this works for you or not. DaVinci Resolve is a great alternative, it's famous for it's excellent colour grading abilities, but since I don't really use it, I don't know much about it.
Once all clips are matched, you can of course choose to artistically change colours for all or some scenes. Like in the The Matrix where they have used a green tint for all scenes that play in the Matrix.