IUPAC nomenclature

Number the chain from the –COOH carbon (C-1): –OH on C-2, ethyl on C-3, C=C between C-3 and C-4, methyl on C-4, C≡C between C-5 and C-6.
$HC\equiv C-C(CH_3)=C(C_2H_5)-CH(OH)-COOH$

When a double bond and a halogen are both present, the double bond gets the lower number.
$Br-CH_2-CH=CH_2$ is numbered from the double-bond end: $CH_2=CH-CH_2Br$ is 3-bromoprop-1-ene.
So the name 1-bromo-prop-2-ene is not according to the IUPAC system; the other three names are correct.

The structure is $CH_2=CH-CH(CH_2CH_2CH_3)-CH(CH_2CH_3)-CH_2-CH_3$.
The parent chain must be the longest chain that contains the double bond; it has six carbons, so the parent is hexene.
Numbering starts from the end nearer to the double bond, so the double bond is at C-1: hex-1-ene.
With this numbering there is a propyl group on C-3 and an ethyl group on C-4.
Substituents are written in alphabetical order (ethyl before propyl).
IUPAC name: 4-Ethyl-3-propylhex-1-ene

The chain has five carbons with one double bond and one triple bond, so the parent name is pentenyne.
The chain is numbered so that the multiple bonds get the lowest set of locants.
Numbering from the triple-bond end gives the locants (1, 3): triple bond at C-1, double bond at C-3.
Numbering from the methyl end gives the locants (2, 4): double bond at C-2, triple bond at C-4.
(1, 3) is lower than (2, 4), so numbering starts from the triple-bond end. In the name, 'ene' is written before 'yne'.
IUPAC name: Pent-3-en-1-yne