Be sure that you added the interaction term (and the main effects) in the Model subdialog and parameter estimates in the Options subdialog. With just one covariate and one dichotomous categorical variable, you are just estimating two separate regression lines. If there is no interaction term, the lines are parallel. the gender=0 * A and gender=1*A terms tell you the two slopes (assuming gender is coded 0/1) The Test of Between-Subject effects tells you whether the interaction is significant.
If you haven't already done so, look in Case Studies>GLM for a short tutorial on how it works and how to interpret the output. That's no substitute for a real textbook, but it's a good quick start.
First, if your design is fully repeated measures, then you have already controlled for gender experimentally. All data is analyzed within subject, and there are not gender differences within subject. Adding gender to the model only further decomposes the between subjects error term, not the within subject factors/error. Of course, there can still be manipulation by gender interactions, but that's separate from controlling for gender. If you meant that your design is a between by within mixed model ANOVA, then the gender covariate will only affect the between subject main effect results. Assuming this is what you mean, I have included the answer below.
You can put it either in fixed factors or covariates. For fixed factors, SPSS defaults to including interactions between all fixed factors. This is probably good since you probably want to know if there are important gender interactions with your manipulation. If there is an interaction, your results are likely much more complex than you hoped for. But there could be important insights there. Also, if there is an interaction, then you violate one of the assumptions of ANCOVA (homogeneity of regression), and you should not analyze the results of a model where you only control for gender.
If you use covariate, make sure you have contrasts set. Though if you only have a M/F gender variable it doesn't matter really. If you have, for instance, male, female, other, and you just had them labeled 1, 2, 3 in your data, SPSS will naturally consider that a numerical variable.
For your other question, I'm unsure what you mean by "importance." If you want to control for gender, you want to analyze only the variance in your DV that could not be explained by gender. SPSS defaults to using type 3 sum of squares, which gives the marginal effect for each variable (i.e. every variable controlling for every other variable). They all have the same importance, but I think this is exactly what you want. If you want a more classic ANCOVA, you would assign all the variance that could be attributed to your covariate first, then analyze the remaining variance for your manipulations. In a sense, gender is treated as more important here. You will get the same results for your manipulations, and the F value will be higher for the gender effect (but in ANCOVA your not really analyzing the covariate anyway). If you treat gender as less important, i.e. only analyzing remaining variance after removing variance attributable to the manipulations, then you're not controlling for gender at all. The results would be the same for the manipulations as if gender was not there at all. So, in short, just use SPSS's default behavior. It is doing what you want it to do.
Last, I want to provide some advice about statistical controls in experimental settings that maybe you don't need, but someone else reading may. First, a categorical control, especially a binary one, will only change results if there are rather large differences in that variable between your conditions (e.g. you have 10 males and 1 female in one group and 10 females and 1 male in another). The problem there is that you are butting up against a failure of random assignment. It is not fully accurate to say that after you control for a variable statistically, you are not only analyzing variance that is purely the result of your manipulations or random error. You can see Miller & Chapman (2001) Misunderstanding Analysis of Covariance and other articles that criticize such interpretations. Second, if there are not large disparities between conditions, but you need to control for something get significant results, then you have entered p-hacking territory, and the validity of your study may be questionable even if you achieve p<.05 in your statistical test. Every textbook I have read on ANCOVA discusses covariates as something you determine beforehand. Determining one after the fact, and after looking at your data is problematic because if your data was significant to begin with you would have stopped there. By continuing to look for ways to make your results significant but not looking for ways to make your results not significant, you increase your true type 1 error rate.
Best Answer
If you want to retain the nominal coding of the Gender variable, you can include it as a fixed factor, then go in "Model...", then select "Custom" (instead of "Full factorial"), and enter all main effects, and the 2-way interaction between score1 and score2, but not the interaction between Gender and either score1 and score2 (i.e., enter only the main effect for Gender).
Alternatively (and this is what I would suggest), you can recode your gender variable into dummy codes or effects code (or any other two values). For example, you could call your variable Female, and code males as 0, and females as 1, and set it as a "scale" variable. Then you could include it in the "Covariates" section.