Why are news headlines written as "He says ..." or "He kills ..." instead of "He said ..." or "He killed ..."?
That is because news headlines are written in a compressed telegraphic style, also known as headlinese.
It might be the best for learners to read this writing style differently from ordinary English. This style has its own special rules of grammar. Short forms, contractions, and abbreviations are usually used. The main reason is to save space.
Here are some useful grammar rules for headlines (the examples are all real news headlines):
Headlines often omit articles and the verb to be.
Venezuelan opposition leader in custody — the leader is in custody
Old London Air Raid Shelter Becomes Vegetable Farm — no articles
Husband Finding Peace After A Terrorist Attack — the husband is finding peace
Most verbs are in the present tenses (as opposed to progressive or perfect forms). The simple present tense is used for both present and past events.
Heavy snow triggers collapse
Obama Wants Tougher Fuel Standards For Big Trucks
Detroit Maps Entire City To Find Bad Buildings
The future is usually expressed as "to" followed by a verb.
Damon Albarn And St. Vincent To Play NPR Music's SXSW Showcase
Comcast deal to face antitrust hurdles
Auxiliary verbs are usually dropped from passive structures.
'Trapped' South Africa miners rescued — the miners were rescued
Yemen: 12 killed, 14 soldiers captured in clashes with militants — 12 people were killed and 14 soldiers were captured
To recap, the simple present tense is preferred. And one good reason to avoid the past tense is because the verb to be is often omitted, which makes the passive voice look like the past tense.
So your tentative headlines could be explained or rephrased like these:
Parliament passes bill — we prefer the present tense
He kills his friend — also the present tense is preferred; using the past tense form could hint the passive voice (see below)
He killed last night — he was killed last night