Regarding your first question: PCA scores are latent variables. From a more general perspective, scale and mean of latent variables are essentially unidentified. Therefore, constraints/conventions are necessary. PCA scores are typically centered at zero such that zero means "an observation that has an average score on the PCA". Negative values just mean "lower than average" component scores. This makes sense because when you conduct PCA on a covariance or correlation matrix instead of the raw data, you essentially remove any information about means from your data (because data are inherently centered in the computation of the correlation matrix).
Here's a minimal example from R for that:
sigma = matrix(0.7,ncol = 10, nrow = 10)
diag(sigma) = 1
X = rmvnorm(n = 200, mean = rep(100,10), sigma = sigma)
fit = princomp(X,scores = TRUE)
Regarding your second question: If you are interested in the value of the component at certain values of the observed variables, you just need to insert these values into the scoring function of the PCA. BUT pay attention that your data is inherently centered when conducting the PCA. The covariance matrix is X'X/(n-1) where X is your centered data matrix. That is, from the perspective of PCA, your data was actually centered. Therefore, I think more discussion is necessary about this point and I refrain from making more specific recommendations without knowing more in detail why you need this.
Edit: Just to be precise. Sometimes PCA is conducted on the uncentered matrix X'X. Then, deviations from the origin also occur as principal components. However, the default in most software packages is to center before calculating X'X and I assumed that you did use some standard software.