white house and more

I don't believe you can actually get inside the White House, I know it shows up on the map as a location but I'm pretty sure there's no way for you to actually reach the inside of the building.

Best way to stay with neutral karma is probably being a good character but when you go into houses, pubs, or any location owned by another person and stealing their stuff, you'll get bad karma and just continue checking your status in your Pip-Boy 3000 to make sure you're not loved or hated.

When you're inside the Jefferson Memorial rotundra, you'll have the option of using the modified H.E.V. Virus that President Eden gives you rather than using the purifier the way it should be used.

The White House isn't a building, it was directly hit by a bomb during the Great War. There is a maintenance or sewer tunnel you go into and follow that and you can get inside the ruins. There is a fat man and 2 or 3 mini nukes along with 1 or 2 glowing ones. There might be a super mutant in there as well.

You can't actually go inside the building. It's not because the game won't let you, it's because all that's left of the White House is a smoldering crator. It was directly hit by a nuke in the great War. Check the sewers around the area and you should be able to access some underground areas of the White House. You'll find a Fat Man this way, but that's about it.

An easy way to stay neutral, I'm guessing you want this for the achievement, is to not be good, and not be evil. This means not killing any innocents, not making any evil quest choices, not stealing anything, not making conversation choices that direct people in a bad way, and not teaming up with bad people. Don't be good by avoiding good paths on quests, not doing good deeds, exc. If you just want the achievements, get to Big Town and have a high speech skill. Talk to her (Save beforehand so not to screw it up) and get her to tell you about her and Pappy dating. Talk to Pappy about this, and you can do a speech challenge to ask him about it. If you have Speech high enough, this should be 100%. But after doing the challenge, the option won't disappear, so you can grind your way up to level 20 without gaining or losing any karma this way. (NOTE: If you fail the speech check, it WILL disappear). Also, if you get the Mister Sandman perk, you can use it on the sleeping boy in one of the houses in Andale and he'll never die, allowing you to grind that way, although that way might give you bad karma.

Lastly, to apply the virus, after dealing with Col. Autumn whichever way you chose, ignore Sara for a minute and go up to the blast door. There should be a machine next to the door. If you didn't give the virus to the Brotherhood, you should be able to use that machine to put the virus in the water.

Hope this helps.