How can we maintain our culture as we increase in company size?

Stay connected by constant communication up and down the various levels of the organization. Executives all the way down to entry level workers need to be transparent and accountable with the decisions they make everyday.

Treat everything equal

Implementing structure, and consequences for poor performance.

Yes - depends on how it will be done but it can be done.

You can't. As you get bigger, changes are done by committee, and mostly things don't get done. OR, they hire a consulting firm to guide the blind.

That can be a difficult thing to do but most important thing to do is instill the culture early in the training process. Hire good fits for the company that blend well with other personalities. A good course to have is RealColors this teaches people what type of personality they are and how to better interact with others of different types. This can build upon a great culture and make everyone feel as though they are a part of the team and help them understand their coworkers.

do not hire people who would drive culture away from current goals. Scaling cannot be maintained, however, the direction can be set

That's a tough one. I'd say through communication and rituals.

You can't. Not entirely. Size changes culture in ways that you cannot prevent. But you can maintain the values that drive the culture you want and accommodate the necessary changes that come with growth while keeping what's important to you.

Ensure companies allocate appropriate funds to maintain / maintain / update their infrastructure and invest in appropriate business systems and people to support the growing employee base. Support functions often have to perform more work with no pay increase and no additional help.