“Oras na upang makipag-ugnayan muli”  = Time to make contact/a connection again.  – Tama  (May also be used to mean, “Time for coordination again”.)

“Sa ngayon, nagpadala ako ng mga mensahe sa aming pinsan, Maryann at Paula.” = As of now/the moment, I sent messages to our cousin, Maryann and Paula.

If what you meant to say was, “I just (now) sent messages...”, then that would be, “Kapapadala ko lang (ngayon) ng mga mensahe...”. 

“... nagpadala ako ng mga mensahe sa aming pinsan...”  - “ako” is “I”, while “amin + g” is “our”.  For consistency, you may want to change “aming” to “aking” (my) (akin + g).

“... aking pinsan, Maryann at Paula.” – In Tagalog, you need to use “mga” to indicate plurality.   Thus, “ang aking pinsan” (my cousin) becomes “ang aking mga pinsan” (my cousins).  Also, if in English we can say, “... my cousins, Maryann and Paula”, in Tagalog, you can’t use the comma for the same effect.  You will need to add the linker “na”, which can mean “which/that/who is/are” depending on context.  In case “na” is used as “who is/are” and it is followed by the name of the person, it becomes “na si” (singular) or “na sina” (plural).

“Kapapadala ko lang ng mga mensahe sa aking mga pinsan na sina Maryann at Paula.” = I just sent messages to my cousins, Maryann and Paula.

Matatas ang Tagalog nila.  = Their Tagalog is fluent. –  You might hear people say it that way, but “matatas” (fluent) refers to one’s ability and not to the language.  Thus, it would be more correct to say it as, “Matatas silang mag-Tagalog” or “Sila ay matatas mag-Tagalog.”  = They are fluent in speaking Tagalog.  Some may say them as, “Matatas sila kung mag-Tagalog” or “Sila ay matatas kung mag-Tagalog”, to mean, “They are fluent when speaking Tagalog.”

Tinanong ko, "Gusto mo bang makipag-Skype?”  = I asked, “Would you (singular) like to have Skype sessions/a Skype session?

Since you are referring to your cousins, a better way to say it would be:  Tinanong ko sila, “Gusto ninyo bang makipag-Skype sa akin?”  or “Gusto ba ninyong makipag-Skype sa akin?” = I asked them, “Would you (plural) like to have a Skype session/Skype sessions with me?” – Also, if we’d say it as “gusto ninyo bang...”, we’d most likely clip the first syllable of “ninyo” and pronounce it only as “’nyo” -> “gusto ‘nyo bang...”.  

“Kailangan ko ng maraming tulong sa aking pagbigkas...” = I need a lot of help in my pronunciation...  - Tama

Oras na upang makipag-ugnayan muli

Sa ngayon, nagpadala ako ng mga mensahe sa aming pinsan <em>na sina</em> Maryann at Paula. <em>Magagaling</em> <em>silang managalog</em>. Tinanong ko, "Gusto mo bang makipag-Skype? Kailangan kong maraming tulong sa aking pagbigkas..."