1.

„Manapság magára valamit adó hollywoodi sztár kizárólag műanyagból készült ruhát, cipőt, táskát, kabátot hord, vagy anyaszült meztelenül pózol az állati jogok védelmét szolgáló kampányban. Valódi bundát újabban egyedül az engedhet meg magának, aki abban jött a világra. Vagy mégsem?”

’Nowadays any self-respecting Hollywood star is wearing clothes, shoes, bags, jackets exclusively made of plastic or is posing in the buff for a campaign serving the protection of animal rights. Lately, only those can afford real fur who were born in it. Or not?’

The literal translation is:
Nowadays on herself something giving Hollywood star exclusively of plastic made clothes, shoes, bags, jackets is wearing, or naked as born by her mother is posing in the protection of animal rights serving campaign. Real fur lately only those can afford who in it came into the world. Or not?

manapság = nowadays
magára valamit adó = self-respecting > this idiomatic expression literally: who gives something on him/herself
hollywood + -i (adjectival suffix)
sztár = star > words used frequently enough are transcribed according to the phonetic writing in Hungarian
kizár (to exclude) + -ó (excluding, exclusive) + -lag (suffix for adverb of manner equivalent to –ly) = kizárólag = exclusively

műanyag (plastic) = mű- (artificial) + anyag (material, substance)
műanyag + -ból (suffix equivalent to the OF preposition because ’to be made’ requires ’of’ and in Hungarian ’készült’ requires ’-ból, -ből’)
készül (to be made) + -t (past tense ending) = készült (used as past participle) = made

ruha > ruhát (accusative case)
cipő > cipőt (accusative case)
táska > táskát (accusative case)
kabát > kabátot (accusative case)
> these words are in accusative case because they are the direct object of the verb ’hord=wear’
hord = to wear

vagy = or
anyaszült = as born by his/her mother
mez (shirt) + -telen (privative suffix) = meztelen + -ül (suffix for adverb of manner) = meztelenül = naked
>anyaszült meztelenül = in the buff, totally naked

pózol = to pose
állat + -i (adjectival suffix) = állati = animal
jog (right) + -ok (nominative plural ending with link vowel) = jogok = rights
védelem (protection) > it is a drop-vowel word due to the –elem suffix. The ending –e of the possessive case is added: védelme. The e becomes é because it is followed by the accusative ending –t: védelmét
szolgál (to serve) + -ó (adjectival suffix) = szolgáló = serving
> az állati jogok védelmét szolgáló = serving the protection of animal rights

kampány (campaign) + -ban (equivalent is the IN preposition but now FOR sounds better in English)

valódi = real
bunda (fur) + -t (accusative ending) = bundát
új (new) + -abb (comparative degree suffix = newer) + -an (suffix for adverb of manner) = újabban = lately
egyedül = only; alone

megenged magának = can afford
-het = can
az, aki = he/those who
az engedhet meg magának, aki = those can afford who

az (that) + -ban (in) = abban = in that/it
világra jön = to be born, to come into the world
mégsem > in this case it should be translated as: not

2.

„A forint az igen kedvező nemzetközi befektetői hangulatban, és a két hónap múlva várható magyar EU/IMF-megállapodás reményétől fűtve a héten jelentősen tovább erősödött amellett is, hogy a Magyar Nemzeti Bank váratlanul nem emelt kamatot valószínűleg az új monetáris tanácstagok ellenkezése miatt.”

’In the quite favourable international mood of investment and fired up by the hope of Hungarian EU/IMF agreement expected in two month, this week forint continued getting stronger significantly even apart from the fact that, unexpectedly, the Hungarian National Bank did not raise interest presumably due to the opposition of the new monetary council members.’

The literal translation is:
The forint in the quite favourable international investment mood, and by the hope of the in two month to be exptected Hungarian EU/IMF agreement fired up this week significantly further got stronger even apart from the fact that the Hungarian National Bank unexpectedly did not raise interest probably due to the opposition of the new monetary council members.

igen = quite, very
kedvez (to favour) + -ő (adjectival suffix) = kedvező = favourable
nemzet (nation) + -közi (inter-) = nemzetközi = international
befektet (to invest) + -ő (noun suffix) = befektető = investor
befektető + -i (adjectival suffix) = investing, of investment
hangulat (mood) + -ban (equivalent to the IN preposition)
és = and
két hónap múlva = in two month
vár (to expect) + -ható (suffix for something made possible) = várható = to be expected
magyar = Hungarian > note that magyar is not capitalized
megállapodik (to agree) > remove –ik and add the –ás noun suffix = megállapodás = agreement

reményétől fűtve = fired up by the hope
> remény (hope) + -e (possessive case suffix equivalent to OF) + -től (equivalent to BY in this case = reményétől = by the hope of
> fűt (to heat) + -ve (suffix for condition now) = fűtve = heated, fired up

a héten = this week
jelentős (significant) + -en (equivalent to –ly) = jelentősen = significantly

tovább = further, on, continues doing
erős (strong) + -ödik (verb suffix) = erősödik = to get stronger
> remove –ik and add –ött (past tense ending with proper link vowel) = erősödött = got stronger
> tovább erősödött = continued getting stronger

amellett = apart from the fact
is = even
hogy = that
Magyar Nemzeti Bank = Hungarian National Bank
váratlan (unexpected) + -ul (suffix for adverb of manner) = váratlanul = unexpectedly

nem = no, not; in this case: did not
emel (to raise) + -t (past tense ending) = emelt = raised
kamat (interest) + -ot (accusative ending with proper link vowel) = kamatot
> nem emelt kamatot = did not raise interest

valószínű (probable) + -leg (suffix for adverb of manner) = valószínűleg = probably, presumably
új = new
monetáris = monetary

tanács = council
tag = member

>tanácstag (council member) + -ok (nominative plural ending) = tanácstagok = council members
ellenkezés = opposition; disagreement
miatt = due to, because of
> az új tanácstagok ellenkezése miatt = due to the opposition of the new council members