Yes, a t-test is necessary to get reliable correlations.

The t-test is a step to count correlations, but modern programs can give the correlation directly. Even in excel you can correlate two variables easily without bothering about the t-test.

It depends on the number of values your research variables has.

If you want to find a CORREALTION, you will need a correlation test. A t-test is only used to determine if there is a statistically significant difference in two groups, and only if the data can be considered continual (taken on a non-arbitrary scale and relatively normal).

First ask yourself, are either of your variables NOT continual data. Examples of numbers that could be considered continual: measurements of time, language proficiency scores, percentages, etc. Examples of number data that are NOT continual measurements: survey question results, Likert-scale results, questions of how people feel about certain things. You said that you measured "communication" and "engagement" but those sound like they were PROBABLY measured in ordinally (e.g. through survey questions) and not continually. If EITHER of these variable were measured this way, you should use a spearman's rank correlation coefficient test. If you have two continual measurements, then you can use a Pearson's correlation test.

Titir Das

I forgot to mention, there are some places where you can conduct these tests online for free, as they are not so complicated. If it is simply two variables.

Here is the spearman's:

https://www.socscistatistics.com/tests/spearman/default2.aspx

Here is the pearson's:

https://www.socscistatistics.com/tests/pearson/default2.aspx