Today I had a lazy day - “Ngayon” normally means “now”, but may also mean “today”, depending on context. You are correct to use “ngayonG araw” as that specifically means “today”. However, “ngayong araw” is really “ngayon na araw”, which means “the day that is now”, but we always say it with the “na” attached to “ngayon”, in the form, “ngayong”. “Lazy day” is idiomatic and won't translate that way in Tagalog. We might say that instead as “Today I felt lazy” = “Ngayong araw tinamad ako”. “Tamad” = lazy, “tinamad” = felt lazy, “tinatamad” = feeling lazy, “tatamarin” = will feel lazy.

I studied Esperanto and a little Tagalog. - The standard prefix for “aral” is “mag” and not “um”. “Mag-aral” = to study, “nag-aral” = studied, “nag-aaral” = studying, “mag-aaral” = will study. “Little” can be “maliit” if you are referring to size (maliit na bata = little/small child) or “kaunti/konti” if you are referring to quantity (kaunting pera = a little/small amount of money). To refer to “studying”, it would be in quantity and not size. “Nag-aral ako ng Esperanto at (ng) kaunting Tagalog” (subject-focused) = I studied Esperanto and a little Tagalog. “Pinag-aralan ko ang Esperanto at kauting Tagalog” (object-focused) also means the same thing, but don't worry about version for now. I only showed you this for you to see when “ko” is used instead of “ako”.

I hope to study more – There would be different ways to say this in Tagalog. “Sana mas mag-aral pa ako” would be its direct translation, but it would sound like you are wishing something for yourself to do more of, but you don't really do it. “Sana mas makapag-aral pa ako” = I wish I'd be able to study more. (This suggests that something is preventing you from doing so). “Gusto ko sanang mas makapag-aral pa” = I'd like to be able to study more. (I think that's what you really meant.)

Ako si Sam

Ngayon araw had ako ng lazy day ay tinatamad ako. umaaral ko yung Inaral ko ang Esperanto at maliit na kaunting Tagalog. Sana, mag-aaral makapag-aral more pa ako.
(what I am trying to say: Today I had a lazy day. I studied Esperanto and a little Tagalog. I hope to study more.)