I view either as unlikely in the extreme. In lieu of immortality, I suggest that it is highly likely that there will be an increase in median lifespan (i.e. more people living longer). There are some incredible challenges to extending the maximum lifespan, mostly due to inaccurate cell replication (deterioration in functionality, malignant cancer growth) and the inability to regenerate some cell types. In the nearer term, some of the physical decline may be further offset through artificial means (biomechanical implants, etc.), but extending the life and enabling the regeneration of neural cells seems to be an incredibly large hurdle, but is probably the most crucial to allow the extension of the maximum lifespan.
Spaceflight seems limited by physics and economic benefit; there is a limit to costs and money that can be spent for ego gratification. A great deal of energy is required to overcome the force of gravity, both for take-off and reentry. This is unlikely to change. There is a limit on the amount of acceleration that the human body can withstand and this is unlikely to change. As a result, the duration in which a biome must be transported and maintained is extended. This helps to drive up costs. Without a large potential benefit, the major factor to drive overcoming this costs comes down to ego, individual or national.
I would predict continued, incremental increases in the average lifespan. I feel that a manned trip to the moon is somewhat likely, but no sustained presence, just one or a small number of short duration missions. I suspect that Earth orbit space stations will also be unlikely; the expenses seem to outweigh and potential manufacturing benefit and the need for human presence for scientific research seems low. There will likely be continued use of unmanned exploration, but not manned.