Don't use the built-in routines of SPSS to conduct a meta-regression (wrong standard errors; does not give you correct model indices; no heterogeneity statistics). Have a look at David Wilson's SPSS "macros for performing meta-analytic analyses". One of these macros is called MetaReg which can perform fixed-effect or mixed-effects meta-regression. I would always use Stata or R. By the way, user Wolfgang is the author of an R package called metafor. This is an excellent piece of software to conduct meta-regression.
As a general (non-technical) intro to meta-regression, I can recommend Thompson/Higgins (2002) "How should meta-regression analyses be undertaken and interpreted?".
Now to your question:
Q1: What is the minimum number of studies necessary for a meta-regression? Some people suggest at least 10 studies are required. Why not 20 or 5 studies?
The answer can be found in Borenstein et al (2009: 188):
"As is true in primary studies, where
we need an appropriately large ratio
of subjects to covariates in order for
the analysis be to meaningful, in
meta-analysis we need an appropriately
large ratio of studies to covariates.
Therefore, the use of metaregression,
especially with multiple covariates,
is not a recommended option when the
number of studies is small. In primary
studies some have recommended a ratio
of at least ten subjects for each
covariate, which would correspond to
ten studies for each covariate in
meta-regression. In fact, though,
there are no hard and fast rules in
either case."
Q2: Is the total sample size an important consideration?
What is total sample size? The number of studies? Yes, it is important. Or the number of individuals? No, it is not (or less) important.
Q3: Why would 10 studies with 200 patients be enough, but 5 studies with 400 patients not be enough?
It is just a(n ordinary) regression. You wouldn't run a regression with 5 data points, would you? In your comment, you state that you have 20 studies which is enough to run a meta-regression.
Q4: Can I enter all three regressors at once and report the global model, or do I have to enter one regressor at a time and report 3 models each one separately?
It is just a regression. I would start with three simple bivariate models then build more complex models (be aware of multicollinearity, see below).
Q5: How does the correlation between the independent variables affects this choice?
A high correlation between your predictor variables will have a (negative) impact on your results. You should avoid that. Please consult a textbook for the problem of multicollinearity.
Q6: How does the number of the studies affect the number of independent variables that I should enter simultaneously?
See the Borenstein et al citation.
Q7: Does the independent variable have to be a scale variable? [...] The independent variable must be also scale, or could be ordinal or nominal?
What is a "scale variable"? Do you mean a continuous/metric variable? You predictor variables can have any level of measurement. However, if you have a categorical (nominal) predictor variable, you will have to deal with dummy variables (see Multiple Regression with Categorical Variables).
Q8: How can I weight my effect size for sample size?
As far as I know, all meta-regression approaches expect the weights to be the inverse study variance, i.e. $\frac{1}{v_i}=\frac{1}{SE_i^2}$. Again, you will need standard errors :-)
Q9: What is the preferable level of significance? Is p<0.05 still acceptable for clinical research in such an analysis?
I cannot answer your question. That really depends on your research question. In my (non-clinical) research I am happy with p < 0.10.
