SJSinNYC, of course on shabbos you should dress more formally than during the week. So on shabbos wear a suit, and during the week wear dress shirt/pants (assuming you’re male). However, you still shouldn’t be dressed informally when davening during the week.
moish01, yarmulkas aren’t just about halacha. In the times of the gemara, only the rabbonim wore them. But today, a yarmulka is a statement. It says, “I’m a jew, and I’m proud”. Once you take off your yarmulka, you’re saying you don’t consider yourself to be a jew. And once you do that, chances are you’re not coming back.