I have created many EPSG shapefiles in QGIS and would like to import them into ArcMap for analyzing.
Can ArcMap open shapefiles made using QGIS?
Yes. Shapefiles created in QGIS are compatible with ArcMap.
However, ArcMap may not understand the projection information that QGIS creates. So watch when you load the shapefiles into Arc, to make sure they have the correct projection. If they don't, you'll have to manually set the projection when you load it into Arc. After you set the projection in Arc, save a copy of the shapefile. The projection should then be saved in a format that Arc can read.
If you're sharing shapefiles created in QGIS with someone who will use them in Arc, be sure to provide them with the information about what projection each shapefile is in. One method is with a README file. A readme is a text file (called README.txt), with information typed into it. The user will have to open the README and, you know, read it. With their eyes.
Here's a sloppy example that I just threw together. Even though it's not in a standard format, it contains the basic information they would need.
This readme file contains metadata about the shapefiles sent by [myname] to [yourname] on [today's date].
layer name: shapefile1
files: shapefile1.shp, shapefile1.shx, shapefile1.qpj, shapefile1.prj, shapefile1.dbf
projection: WGS 84 EPSG:4326
layer name: shapefile2
files: shapefile2.shp, shapefile2.shx, shapefile2.qpj, shapefile2.prj, shapefile2.dbf
projection: WGS 84 / Pseudo-Mercator EPSG:3857
If you hate the person you're sending this data to, make sure every layer is in a different projection. (Conversely, if you don't hate them and/or want to behave with basic human decency, use the same projection for all the layers.)