Hi, I will try to help you with some of the questions.
Is salvation synonymous with going to Paradise? When Heaven is mentioned, is that also Paradise? Please also list any other words/synonyms used, whether English or as mentioned in the Qu'ran.
Yes salvation is synonymous with going to Paradise, since in Islam we don't have anything like salvation by grace of God. We attain salvation (heaven) by working hard and believing in God. Heaven is also Paradise, correct. Jannat is the arabic word for this or Jannah and also Garden or Gardens although the last two are rarely used. Sometimes we will also use the words Hereafter, afterlife or akira (arabic, sorry that's not the correct transliteration) to refer mostly to Heaven and not just Heaven AND Hell. I will also like to add that there are seven levels of Heaven in Islam.
What are teh conditions for going to Paradise? Are they different for men and women? Who can go to Paradise?
The conditions to going to Paradise are believing in the One God (as well as the other articles of faith such as belief in Judgment Day, scriptures, prophets, angels, divine decree) and doing good deeds. There is no difference for men and women although the good deeds themselves might be slightly different. For example, a good deed for a man might be treating his wife in the best way possible while a good deed for a women might being modest and covering up. Anyone who does righteous and believes in God can go to Paradise, this is not a Muslim only zone. Hypothetically though, God will not treat unjustly those that never heard about the One God or the message of Islam. He will judge them based on their intentions. Therefore, it is possible for someone that did not believe in God (because they never heard the message) can go to heaven. There is a hadith somewhere regarding this but I can't find it at the moment, something about a baby, blind man and??
What is obtained in Paradise? Is this different for men and women?
Please read this site. Most of the statements are directly from Quran or the authentic hadith sources:
http://www.geocities.com/mutmainaa1/belief/paradise_description.html
In a nutshell though, you get whatever you want and also you cannot imagine Heaven. Whatever you imagine it to be, it is better than that. But the best part is that we will get to meet Allah one day.
I have read somewhere on this forum that all Muslims are entitled to enter Paradise even if they have sinned. Is there a source for this? (Whether scriptural or from a trustable website)
It is in our belief that anyone who sincerely believes in God will eventually enter Paradise, but might have to clear away their sins first by entering Hellfire. The Sahada "There is no God but God and Muhammad is His Messenger" is the testimony of faith that all Muslims adhere to.
1. The Prophet -- Allah bless and greet him -- said: "Whoever says: there is no god but Allah enters Paradise." Tabarani narrated it from Abu Dharr in the Kabir (7:55), Ibn Hibban in his Sahih (31), al-Hakim in his Mustadrak (4:251), al-Mundhiri in al-Targhib (2:422), al-Haythami in Majma` al-zawa'id (1:18), Ibn `Adi (7:2639), Abu Nu`aym in the Hilya (7:174), and al-Bazzar from `Umar.
2. The Prophet -- Allah bless and greet him -- said: "Whoever says there is no god but Allah enters Paradise even if he commits adultery and even if he steals (i.e. even if he commits great sins)." (Nasa'i, Tabarani and others from Abu al-Darda' - sahih).
3. The Prophet -- Allah bless and greet him -- said: "Whoever witnesses that there is no god but Allah and that Muhammad is Allah's Messenger, Allah forbids the Fire from touching him." Narrated by Bukhari and Muslim from `Ubada ibn al-Samit.
Ibn Hajar in Fath al-Bari, book of riqaq ch. 14 (1989 ed. 11:324) says that the hadiths of "Allah forbids the Fire from touching him" are even more explicit than those of "Allah will enter him into Paradise" in establishing that the one who declares Allah's oneness is saved even if he does not heed the orders and the prohibitions.
Is there any concept of becoming 'one with God' in Islam?
Hm...I'm not exactly sure what you mean by this, can you please clarify?
This is unrelated, but what do Salaam Alaikum and Walaikum Salaam mean?
Salaam Alaikum is the Islamic way of greeting which means "peace be unto you" and Walaikum Salaam is the response which means "and peace be unto you too"