Arise (arising, arose, arisen) is an intransitive verb, just like arrive, happen etc:

(1) To come into being; originate: ‘A new religious movement originated in that country’; ‘The problem first arose when I tried to get a visa.’

(2) To spring or proceed as a consequence; result: ‘A slight discontent arose from this discussion’; ‘When there is a clear written agreement, misunderstandings do not arise.’

(3) To move upward: ‘The smoke arose from the forest fire.’

(4) To get up and stand up from sitting, or lying position: ‘I arise at 7 A.M. every day’; ‘They arose early’; ‘The audience arose to applaud the performance.’

(1) A statement, reason, or fact for or against a point: ‘He presents a strong argument in favor of reservation issue.’

(2) A discussion involving differing points of view; debate on some proposition or proposal:  ‘Economists were deeply involved in an argument about inflation.’ The argument over dowry system goes on and on.’

(3) A process of reasoning; series of reasons: ‘I couldn’t follow his argument.’

(4) An oral disagreement; verbal opposition; contention; altercation: ‘They were involved in a violent argument.’

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Appear = (1) Become visible or be seen (suddenly): ‘Small red patches appeared all over the child’s back.’ ‘A minute later the manager appeared and asked what was wrong.’ (2) Become available or be seen for the first time (Of something new): ‘The first edition of the book appeared in 1987. ‘The new model will not appear in the shops till the end of the year.’(3) To stand formally in presence of some authority, tribunal, or superior person to answer a charge or plead a cause: ‘He must appear in the court today.’(4) To have the appearance  of being; seem; look: ‘She appears nice today’. (5) To be obvious or easily perceived; be clear or made clear by evidence: ‘His comment appears convincing to me.’

“Anyhow” and “anyway” are used to connect sentences only in informal styles (Not in essays, written reports, etc). Their main uses are: (1) to show that you are about to return to the main topic or story line: ‘Anyway, as soon as the plane landed he was rushed off to hospital and that was the last I saw of him,’ (2) to show that your next point is just as important or relevant as your last one; ‘Anyway, I’m too busy to play tennis this afternoon’. ‘Anyhow, it looks like it’s going to rain.’

Anxious = worried because you fear that something bad may happen or may have happened: ‘Their daughter hadn’t come home from school and they were anxious about her safety.’ ‘I knew it was just a minor operation, but I couldn’t help feeling anxious.’

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When you want to give people some important information, you make announcement: ‘Following the announcement of their marriage, they were pursued by crowds of journalists.’

An advertisement is an item in a newspaper, on television, etc, that tries to persuade people to buy something, apply for a job, etc: ‘At this time the year, the papers are full of holiday advertisement.’

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