Let me start by suggesting that it might be good for both you and your new partner to go (together if at all possible) to go for a sexual health check which includes screening for STIs.  This is not an accusation but simply acknowledgement that both of you appear to have had other partners in the past, that many STIs can occur without symptoms, and that while it is unlikely that either of you are infected, knowing this based on mutually negative tests will provide a measure of confidence and trust as your relationship moves forward.  We routinely recommend this for new relationships and suggest that such testing should include testing for gonorrhea, chlamydia and for the woman and sometimes the man, depending on the test performed, tests for trichamonas using either vaginal swabs of for the male a urine test.  Testing for HIV and syphilis, while far, far less likely can be easily added with a blood test if desired.  We specifically recommend against blood tests for herpes unless one partner has a history of the infection as they have relatively frequent false positive test results and can be misleading. In the US confidential testing can be obtained for little cost at health departments.

My other general recommendation for you (and if possible, your partner) is to be sure you have been vaccinated against HPV.  The vaccine is highly effective and safe. 

1. The cdc and most doctors (from what i can tell) do not recommend testing for hsv without symptoms. Is this correct and if so, why? What do you recommend without symptoms? 

Please see my comment above.  I strongly recommend against testing in this situation.

2. I have seen that condoms do not protect against all stds, like herpes, hpv, etc. How effective are they at protecting one from such stds? Do they decrease the risk substantially? 

Condoms remain the most effective means of reducing risk for acquisition of all STIs if one is exposed.  The amount they protect varies depending on the STI we are speaking about.  For STIs spread in genital secretions like gonorrhea, chlamydia, trichamonas and HIV, when used throughout sex without breakage, they provide well over 98% protection.  For the so-called "lesion" STIs like syphilis, HSV and HPV they are somewhat less protective, reducing risk in the range of 60% or more because the lesion may not be covered by the condom.

3. Is there any other way i can protect myself? I know that taking prep can reduce your risk of contracting hiv, so is there any similar thing for other stds? 

If your partner does not have HIV, I would not recommend chronic PrEP and see no need for PEP for most people with regular sex partners. 

I hope these comments are helpful.  EWH