The more qualified the role, the more leeway there is to negotiate the salary. Most employment conditions in Sweden are regulated by collective agreements, with the result that there is little room for individual negotiations, at least for lower skilled jobs.
Pay on a monthly basis is the most common. For management positions there may be scope to negotiate non-statutory benefits; these would be discussed with the HR department.
For jobs in government and with children, proof of good conduct is required. This will be stated in the ad or the employer will inform you.