Adding field in table counting from different table using QGIS

I just started to work with QGIS recently and am struggling with the following:

• I have 1 a CSV table on offshore branches of certain institutions including info on their respective countries of origin. No geographical data except the columns with country names (Home Country, Host Country).

  Here is an example of the table with the relevant columns:

• I also have 2 a polygon layer with the world countries in which each country takes 1 row, and each with it's own polygon represented in the shapefile (the country name column is named name)

Both attribute tables use the same format for the country names.

Now I would like to

1. add a field (column) to the 2 country layer's attribute table that counts for each country how many institutions have it as a Home Country in the CSV table. Using the above table as an example, the new column would count 2 for Germany, and 1 for USA.
2. add additional columns to the 2 country layer's attribute table that count for each country how many institutions have it as a Home Country in the CSV table AND have a branch in a certain Host Country. For example in the above table I would like to only count for those countries with institutions with a branch in Host Country = India. The resulting column should count 1 for Germany, and 1 for USA.