The meta analysis obviously different from review of literature. What would be the possible methods for meta analysis? Does meta analysis need the software for analysis or it can be done by different procedure ?
Answer to your fist question: You can adopt an equivalence: your studies comparing means (or proportions) of independent groups with cross-sectional studies and hence apply meta-analytic techniques to aggregate cross-sectional studies.
Answer to your second question: You can use a specific software like REVMAN or build the graphics of meta-analysis (Forest Plot) using R software, for instance. I recommend REVMAN. You can download it (free) from the website
There are 2 possible methods for meta regression analysis.
FAT-PET and PEESE.
For detailed information see,
1. Gök, A. The role of financial development on carbon emissions: a meta regression analysis. Environ Sci Pollut Res (2020). https://doi.org/10.1007/s11356-020-07641-7 for FAT-PET
2. Ugur, M. (2014). Corruption's Direct Effects on Per‐Capita Income Growth: A Meta‐Analysis. Journal of Economic Surveys, 28(3), 472-490. for FAT-PET and PEESE.
The analysis is simply weighted least squares, you can use Stata and regress command.