1. How do native Norwegians feel about American-born Norwegians returning to Norway? In general, are they accepting and welcoming of people from other countries moving to their country?
While in America you might be "Norwegian American" or tell people that you're Norwegian, unless you've got a Norwegian passport, then you're an American - you won't get any special treatment for having a Norwegian bestemor. Acceptance of immigrants varies. The second largest party in the current parliament stands on an anti-immigration platform, and makes no bones about introducing discriminatory laws or using existing laws in a discriminatory way. On the other hand, the largest party and the third largest party (who look like they will lead the next governemnt) are quite happy to have immigration. But just like in the US, some people will be dead against immigration, and others will want open-borders. Generally, those who are anti-immigration are in the minority, although they may be more vocal. If you speak the language, make an effort to integrate, then you'll be fine.
2. Must one be able to speak Norwegian in order to be considered for employment?
It depends. If you have a skill which is in high demand (engineering, techinical skills) then you can find employment without Norwegian. If you are happy to work a low-skill, low-pay (by Norwegian standards, 120~kr/hr) job like waiting tables or bartending, then again, you can find employment without Norwegian. There will however, be a certain amount of pressure to learn Norwegian, which you should of course do anyway, since you're going to be living here. Being able to speak Norwegian will also increase your jobs chances.
3. Obviously, I would need to have a job lined up before moving. Does anyone know what the job market is like currently for landscape architects and architects? What resources are available to assist in locating employment? What cities may be the best for landscape architects and architects?Â
No idea about this one, sorry! But if I were looking for a job, I'd start by looking online for companies that work in my field.
4. Is a professional with a college degree able to afford his or her own apartment, or would you likely need to find roommates?
You will be able to afford to rent an apartment, but it will take up a significant part of your after-tax income (about a third to half) if you're not sharing the burden with anyone. As in the US, there are expensive areas and less expensive areas. As a rule, areas with an above-average immigrant population and student population are generally cheaper (and more immigrant friendly).
These answer reflect only my view and experiences. It's important to get the views of others, so hopefully more people will reply to your post.