NextStep consisted of the Mach microkernel, BSD (probably the 4.3 release, and updated to 4.4 and Net/2 when later available), and some other technologies outside the BSD arena. After Apple purchased it, it probably contained whatever the latest free BSD code was available...4.4 BSD-Lite, probably, since 386BSD was the original BSD port to Intel hardware (from which FreeBSD was derived)/ Darwin was Apple's open source release of their [then] current version of Mac OS X...Cheetah, I think? I played with a copy of OS X server when it was first released in 1998, and found the command-line remarkably similar to FreeBSD 2.x (though I was not an expert and the BSDs have kept many BSD-isms throughout the ages). Apple had probably integrated the latest BSD derivative available for that Mac OS X release. I remember reading about a switch to from FreeBSD 3.x to 5.x in the Panther release notes or somewhere similar, so they had long since switched to FreeBSD from whatever NextStep used by the time Darwin was released.

So, no. Darwin wasn't originally based on FreeBSD. Darwin was the source code based on released version Mac OS X, which was originally based on NextStep/OpenStep, which was based on Mach/BSD, which existed before FreeBSD.

The Apple Darwin kb page linked above is part of Apple's (now-defunct) attempt to drum up interest in Darwin as the core of Mac OS X, but wasn't a fork of 4.4BSD as the AC post above implied.

Here are your options:
1. Get free hosting elsewhere. Pick a random hosting compnay. You can get nearly any cheap-ass web hosting company to offer you a "free" account which will likely be on shared hosting. Your service probably won't improve. If your code is the problem, you'll experience the same issue at your new host. Lather, rinse, repeat. Keep switching until you do one of the three options below.
2. Work with a larger hosting company who is more B2B oriented to obtain free / reduced cost / sponsored hosting. Tell them your problems *up-front* and what you need help with. You'll likely be talking with a Marketing department who is willing to sponsor the hosting costs, so they won't actually know anything about your problems or how to fix them without engaging support/operations. They may be able to refer you to someone internally or externally who can help, and you may get better support or assistance (or maybe not - tell them upfront what you need so they can tell you upfront what they'll help with. "SLAs", ya know?).
3. Find a volunteer developer/admin who is willing to help you troubleshoot. If you can't afford to pay someone (as recommended many times above), then this may be a good alternative. There are local user groups in your area for PHP, Python, Wordpress, Drupal, Joomla, Java, etc. Figure out what's running your website and start attending the relevant meetings. Start networking and making friends in the communities if you can't afford to hire a professional outright. But be wary of less-knowledgeable assistance from a volunteer who may steer you in the wrong direction during the troubleshooting process - he may tell you that you need to do X or Y, when in reality, he don't actually know shit and is just recommending different things to hide his inexperience.
4. Pay for real hosting and/or a real contractor to assist you. Money solves a lot of problems. If you're a large, multi-national non-profit and your brand is at stake, this is your best bet. What is "real" hosting? The best hosting service you can afford, with the level of service you need. This could be a managed, B2B provider or just a guy running services out of a rack in a local datacenter. No one here can tell you what's right for you without further consultation.

I've worked for both shared hosting companies and enterprise-level managed hosting companies. Both support non-profits, and both go about it very differently. Start talking to them and see what you can get. And attend those user groups! You'll find an amazing wealth of knowledge and resources there.

He didn't say he wasn't using professionals, but that he was looking for "ideas or best practices". Sounds to me like he's in charge of the project for his company, but will be using contractors (such as designers/architects, consturction crews, etc) for the actual work.

The interior designers and architects will know how to design a layout based on his input and requirements, but they may not have specialized knowledge for his particular use case. He's looking for ideas from people who have been in the trenches and can tell him what has and hasn't worked for them in the past. He may read of a particularly good idea that he didn't think about (and that the architect might not have suggested), and he can incorporate it into his requirements. *Then* the architect can design accordingly.

Also think about ingress/egress. If you're trying to carry equipment like rack-mount servers, you'll want elbow room to bring it in the door. Go for double-doors in the entry-way without that middle door jamb, so they can both open up to create one massive entry-way. This is useful when two people are carrying a heavy 4u server or when you need to roll in gear on a cart or handtruck.