It is very difficult to diagnose without knowing which one is categorical, binary, and continuous.
If a categorical variable has k levels, you only need (k-1) dummies to capture the information. If you fit all k of them, SPSS will throw one out. The reason is that if all k are present, the whole set are perfectly collinear, standard errors will then get too big; the model, fail.
Another reason for some others being excluded is probably their information was already perfectly captured by other variables. For instance, you "LAW" categorical variable may be already perfectly explained by the country dummies because it's very unlikely that a country will have two equally superior official languages or law systems.
I think overall, the analysis presented here is too hasty. I'd suggest checking some tabulations between predictors to better understand if there is any exclusiveness going on. Fit the model step by step manually to observe any change.
The regression in the OP shows that US-based companies have a negative
relation to CSR score, and UK-based companies have a positive
relation. In my dataset, 170 out of 475 companies are US-based. All
other english-law based companies have only about 100 companies
between them. How can it be that if most of english law-based
countries have a negative relation to CSR score, in the regression I
linked to, the english-law variable is actually positive (.740)?
There can be many reasons.
Regression takes into account of group size AND the actual data each case brings to the table. A smaller group like UK can still drag the average if their firms has a very large and positive score, if the US firms' scores are mediocre.
The reference groups in the two models are different. In the linked output, the reference group is all non-English countries. In the above output, the reference group are all other 18 countries that were not included in the model. Since UK and US are probably not the only two countries practicing the English system, changes in their mean estimate may be possible.
Different control variables can also change the estimates, an exception is when the control variables are totally independent from the main predictor, which in this case is unlikely.