I studied in the UK between 2006-2011, unfortunately in 2011 while trying to apply for a post study work visa, Immigration officials found anomalies with my bank statement and they had to remove me from the UK. I am now resettled in my country and my circumstances have changed. I may be required to travel to one of the EU countries (Sweden) early next year. I am just concerned if my application may be denied based on the past circumstances.
You were removed from the UK in 2011 when you made an application for a post-study work visa and they determined that you had submitted a forged document. You do not have your removal paperwork, and hence do not know the conditions of your removal. You may need to visit Sweden and want to know if your removal will have a pejorative effect on your application.
The first step is to recover the information surrounding your removal to find out if you have been placed on an exclusionary register. To do this, you can file a Subject Access Request with the Home Office and wait for their reply. This can be frustrating because you will need to clear identity hurdles imposed by the Data Privacy Act and several exchanges of correspondence may be needed. Having cleared all the identity hurdles, they may opt to refuse your request. They would do this if you have been placed upon an exclusionary register. If this happens you will have to take it up with the Ministry of Foreign Affairs in your own country because you have no further recourse with the UK (or any other country the UK exchanges information with).
If they reply, you should then take the information to a specialist practitioner in the Law Society for a consultation. They will be able to tell you if a ban is currently in effect and the extent to which you are vulnerable going forward for the rest of the EEA. Your selection of a practitioner should be informed by the list of firms that have a branch office (or correspondence status) with Sweden. The list is here.
For the UK part of your question and given that a ban is not currently in effect, the next time you apply, the ECO will be required to place a mandatory ban under Paragraph 320 (11) (where the applicant has previously contrived in a significant way to frustrate the intentions of the Rules by:...) (emphasis mine). There is no discretion permitted.
For the EU part of your question, the UK is a participant in the Schengen Information System and is required to place an alert entry in SIS whenever an in-country removal has been ordered. Both an alert entry and exclusionary entry are causes for Schengen refusals. Depending upon the circumstances of your removal, the UK may have also made an entry in the European Criminal Records Information System and this will also prompt a refusal.
For your tacit question about 'change of circumstances', your solicitor will know how to frame this change in a positive and convincing light and to provide the necessary supporting documentation such that you have a better chance of success (but not guaranteed). I estimate that the 'all-in' costs for consultation and subsequent application would start at about £700 and range to about £1,500 depending upon their competence in the field and other complexities in your case.