As I said elsewhere, in my experience, people write in longhand using the proper accent marks and punctuation, but tend to leave that out when typing except when the occasion calls for it, as in, for example, when typing a CV or a formal letter.
Leaving out the accent marks seldom produces confusion, but it may pose a problem in some cases. Sí ("yes") vs. si ("if") is one notorious case. The diaeresis over ü is definitely not a problem. I'll be hard-pressed to think of a word that could conceivably be misread due to its missing a diaeresis over u.
Most if not all people will leave out the opening question and exclamation marks when typing. Most will also leave out the full stop after a paragraph, and many will substitute a comma for a stop in mid-paragraph. Many drop the stops and commas altogether, which sometimes makes for confusing texts.
Further simplifications are common as well; some are only found in typed texts, while others have been common in fast handwriting (such as in note-taking) for ages (e.g. substituting q for que).
Spanish-language natives recognize ñ as an individual letter distinct from n; the tilde ~ over ñ is not counted among the accent marks, and is never left out.
One would think that predictive dictionaries and autocorrect software on most devices should be enough to avoid the disappearance of accent marks, at least (e.g. if you type lapiz aleman on your cellphone, the autocorrect should change it immediately to lápiz alemán), but it seems that's not happening. There are many Spanish words (especially verbs) that are correct both with and without a given accent mark, which surely explains why the autocorrect doesn't do its job, since it has no real contextual awareness (if you write tiro, it has no way of knowing whether you really meant tiro "I throw" or tiró "he threw").