Can I get a mammogram if I am still breastfeeding my baby?

No. Most likely getting a mammogram while nursing will not be helpful, since you have increased size of the breast glands and you might get flagged as a false-positive. Also due to the nature of the machine (mashing on the breasts) it could be quite messy.
You can, but ... The likelihood of inaccuracy (in this case, a false negative result) is higher owing to the increased density of the breasts during lactation which can mask subtle disease like a small nodule. If there is a focal area of concern, than ultrasound can be performed of this area. Feel free to read more here: http://www.Conciergeradiologist.Com/mammogram-guidelines.Html.
No. No. Do not rec a mammo while breast feeding. Consider ultrasound as it has no radiation exposure risk.
Mammo. If you have a mass or other symptom that needs to be evaluated, yes. If you are just due for screening, you are better off waiting 6 months or so following cessation of breastfeeding, because the lactational changes of the breast will create mammographic changes that may be difficult to interpret.
Can but not helpful. Because you are lactating the breast tissue will be substantially denser and the effectiveness of the mammogram will be reduced. In addition, it may be significantly more uncomfortable. Consider waiting until you have stopped lactating.
Yes. Three % of breast cancers are found during pregnancy or lactation. Mammography is safe during lactation, but may not be as accurate. Negative studies should have a back up study such as ultrasound ANS or needle biopsy if a suspicious mass is found. See "the physicians pocket guide to breastfeeding", breast masses, texas dept of state health services, 2005.