Existence. . . .  pag-iral (more philosophical term); pagkakaroon

(more street-level); pananatili (with an additional sense of "continued existence") Existing. . . .umiiral

Life. . . . . . . buhay

Being [noun]. . .ka--[h]an, or pagka--, or pagiging --; this needs a bit more explanation "I have to know your whole being. " = "Kailangan kong malaman ang but to mong pagkatao/katauhan. "

"Being precedes thinking. " = "Ang pagiging [tao, bagay] ay nauuna sa pag-iisip. " In this context, "being" = "pag-iral" would also fit.

Being [verb]. .  no exact equivalent; the sense of "being" is reflected in the conjugation of whatever word the verb itself links up with.

I am being frank with you. " = "Ako ay nagiging tapat sa iyo. "

(Or, more idiomatically, "Tinatapat lang kita. ")

I  was. .Ako ay [the past tense resides either in verb conjugation, or in a time-describing adverb]

 I was blind." = "Ako ay naging bulag"(Literally, "I became blind. "] or "Ako ay bulag dati/noon. " (Literally, "I [am] blind previously. "

He was. . .Siya ay [same as above]

They were. . Sila ay [same as above]

I am. . . Ako ay [the present tense resides either in verb conjugation, or in a time-describing adverb; or else, a time-independent sense that applies to the present is assumed].

 I am a Filipino" = "Ako ay Pilipino. "

I am outside the house." = "Ako ay nasa labas ng bahay. "

I am thinking." = "Ako ay nag-iisip. "

You are.  Ikaw ay [same as above]

He is. . Siya ay [same as above]

They are. . Sila ay [same as above]

 I will be. Ako ay mag-- or Ako ay magiging -- or Ako ay [verb in the typical Pilipino form of future tense]

I will be attending class tomorrow. " = "Ako ay dadalo sa klase bukas. "

I will be an astronaut someday." = "Ako ay magiging astronot balang araw. "

He will be. . Siya ay [same as above]

They will be. . Sila ay [same as above]

There was. . .Merong -- or May -- [coupled with noun or verb in past tense] 

There was an old woman who lived in a shoe. " = "May isang ale na nakatira sa sapatos."

There will be. Magkakaroon.

There will be dancing after dinner." = "Magkakaroon ng sayawan matapos ang kainan. "

It existed. . .Umiral ito.

The boy is being kind = Ang batang lalaki ay [nagiging] mabait. Or more idiomatically: Ang batang lalaki ay nagmamagandang-loob.

The building has existed for ten years = Ang gusali ay [umiral, nanatili,  nakatayo] ng sampung taon.

The girl is running quickly = Ang batang babae ay [tumatakbo] nang mabilis.

The boy will be handsome = Ang batang lalaki ay [magiging] guwapo. Or more idiomatically: Ang batang lalaki ay [lalaking] guwapo (where the "lalaking" in brackets is literally "will grow up to be")

The man was a doctor = Ang lalaki ay doktor [noon, dati].

I believe in the existence of atoms. = Naniniwala ako sa [pag-iral] ng mga atom.

Life exists on earth. = [Umiiral] ang buhay sa mundo. Or, more street-level:  [Mayroong] buhay sa mundo.

I like being a student. = Gusto ko ang [pagiging] estudyante. Or, more idiomatically: "Gusto ko na estudyante ako. "

I enjoy living my life. = Masaya ako sa aking buhay (Literally, "I enjoy my life" where there is no "existence" term), or, Masaya akong namumuhay

(Literally, "I enjoy living. ") The literal translations "Masaya akong namumuhay ng aking buhay" or "Masaya kong tinatamasa ang aking buhay" are somewhat awkward.

I love him/her with my whole 'Being. ' = Iniibig ko siya ng but to kong [pagkatao].