P = NP question

I was skimming through Sipser the other day and came across an anomaly I believe I may have encountered before (I think I recall reading this sometime in 1997 for the first time). It points to something I dont quite understand about the P = NP question so I decided to do some scribbling on a note pad and type it up in latex.

The question I had points to the following:

1) Why don't TM based trie (radix-tree) like data structures trivially decide any language in O(n) time (and thus yield a trivial solution to P = NP since every deterministic Turing Machine is a nondeterministic one)?

2) If this is the case it would seem that there is something wrong with the definitions of NP and P in that having a DTM or NTM decide a language may not be strong enough to capture what someone means by a language.

3) There are obviously cases of languages that seem to be decided by algorithms which are in NP but not P. An example would be something like a generalized password cracking tool akin to John the Ripper(for those security gurus).

I tossed it up on google docs here:

I am curious if there was anything wrong with my reasoning.